30th Marian Smoluchowski Symposium on Statistical Physics

3 Sept 2017, 08:00 → 8 Sept 2017, 18:00 Poland

On the Uniformity of Laws of Nature

The 30th anniversary symposium is celebrated as an EPS conference of the Statistical and Nonlinear Physics Division

 

Year 2017 has been proclaimed by the Polish Physical Society as the Marian Smoluchowski Year, to commemorate life of the outstanding physicist (1872-1917) and his influential scientific contributions to physics, mathematics and contemporary science.

The scope of the 2017 Symposium will cover:

• Nonequilibrium systems with large fluctuations and strong correlations
• Stochastic and quantum thermodynamics
• Fluctuation relations and large deviation theory
• Decoherence, chaos and quantum-classical correspondence
• Diffusive processes and weak ergodicity breaking
• Fluctuation-dissipation relation in fluids, granular media, nano- and biological-systems
• Active matter, collective phenomena in living systems
• Nonlinear dynamics and turbulence
• Complex networks
• Simulations and modeling in polymer physics and soft matter
• New frontiers in contemporary statistical physics Interdisciplinary applications

Monday, 4 September

Session 0: Opening

Convener: Prof. Ewa Gudowska-Nowak

1 Opening

2 Marian Smoluchowski his life and works

$\;$

Speaker: Bogdan Cichocki (Instytut Fizyki Teoretycznej Uniwersytetu Warszawskiego)

3 Arrays of coupled two-state oscillators

We discuss synchronization of arrays of coupled two-state stochastic oscillators with additional fluctuations due to finite numbers of units, types and ranges of couplings, memory effects, etc. If time permits we present phase diagrams

Speaker: Katja Lindenberg (University of California, San Diego)

10:30 Coffee Break

Session 1

Convener: Prof. Ewa Gudowska-Nowak

4 Entropy facilitated active transport

We show how active transport of ions can be interpreted as an entropy facilitated process. In this interpretation, a particular change in the pore geometry through which substrates are transported gives rise to a driving force. This chemical energy provided by the chemical reaction is then used to create a protein geometry favorable for the uphill transport of ions. Attempts to estimate the energy available by this change in several proteins shows that an entropic contribution from the pore geometry is significant. We discuss how this effect can be used to understand how energy transduction in active transport can take place over a relatively long distance.

Speaker: J. Miguel Rubi (University of Barcelona)

5 (Quantum)-Thermodynamics at strong coupling and its implications for Stochastic Thermodynamics

The case of strong system-environment coupling plays an increasingly seminal role when it comes to describe systems of small size which are in contact with an environment. The commonly known textbook situation refers solely to a weak coupling situation for which the equilibrium state of the system is described by a Gibbs state. This situation changes drastically, however, when strong coupling is at work; then, the interaction energy can be of the order of the (sub)-system energy of interest [1]. Let us consider first an overall thermal equilibrium of a total setup composed of a system Hamiltonian $H_{S}$, coupling Hamiltonian $H_{int}$ and a bath Hamiltonian $H_{B}$. Based on an explicit knowledge of the so termed *Hamiltonian of mean force* [2], the classical statistical mechanics and, as well, the quantum thermodynamics of open systems which are in contact with a thermal environment -- at arbitrary strong interaction strength -- can be formulated. Yet, even though the Hamiltonian of mean force uniquely determines the thermal phase space probability density (or the density operator, respectively) of a strongly coupled open system, the knowledge of this quantity alone is *insufficient* to determine the Hamiltonian of mean force itself; the latter must be known for constructing an underlying Stochastic Thermodynamics. This fact presents a major stumbling block for any classical Stochastic Thermodynamics scenario which solely builds upon the knowledge of (observed or calculated) open system trajectories. -- In the classical case we demonstrate that under the assumption that the Hamiltonian of mean force is known explicitly, an extension of thermodynamic structures from the level of averaged quantities to *fluctuating* objects (such as internal fluctuating energy, heat, entropy, or free energy); i.e., a Stochastic Thermodynamics, is possible. However, such a construction is by far not unique but involves a vast ambiguity. Generally, however, the situation becomes a No-Go if we consider an initial nonequilibrium where even the concept of a Hamiltonian of mean force does not exist [1, 3]. $ $ [1] P. Talkner and P. Hänggi, Open system trajectories specify fluctuating work but not heat, Phys. Rev. E 94, 022143 (2016). [2] M. Campisi, P. Talkner, and P. Hänggi, Fluctuation theorem for arbitrary open quantum systems, Phys. Rev. Lett. 102, 210401 (2009). [3] H. Grabert, P. Talkner, and P. Hänggi, Microdynamics and Time-Evolution of Macroscopic Non-Markovian System, Z. Physik B 26, 389–395 (1977).

Speaker: Peter Hänggi (University of Augsburg)

6 Life at the edge, complexity and criticality in biological function

The organization of biological form and function is a classic problem, cut-crossing disciplines, which include a variety of complex spatiotemporal patterns. Historically, work focussed first into the understanding of self-organization and later attention shifted to scale-free collective fluctuations, many of them shown to correspond to critical phenomena. In that context, I will review our work on critical dynamics across several scales uncovering novel understanding of proteins, mitocondria and brain function.

Speaker: Dante Chialvo (Center for Complex Systems & Brain Sciences (CEMSC3). Universidad Nacional de San Martin & CONICET. San Martin, Buenos Aires, Argentina)

12:30 Lunch Break

Session 2: Panel A

Convener: Prof. Peter Hänggi (University of Augsburg)

7 Dynamics of classical isolated disordered systems

We study the dynamics of classical disordered macroscopic models completely isolated from the environment reproducing, in a classical setting, the ‘quantum quench’ protocol. We use two classes of models, distinguished by the complexity of their energy landscape. We identify quenches after which the evolution approaches a stationary state that can be associated to equilibrium at a single temperature (related to the energy change during the quench), cases in which an ageing asymptotic dynamics persists asymptotically, and quenches in which a steady state characterised by a Generalised Gibbs Ensemble is found. In the latter case we show that all the GGE effective temperatures can be obtained from the standard fluctuation dissipation relation, in the frequency domain. The parameter dependence of the asymptotic states is rationalised in terms of dynamic phase diagrams. $\;$ [1] Leticia F. Cugliandolo, Gustavo S. Lozano, Nicolas Nessi J. Stat. Mech. (2017) 083301. [2] Laura Foini, Andrea Gambassi, Robert Konik, Leticia F. Cugliandolo Phys. Rev. E 95, 052116 (2017)

Speaker: Leticia, F Cugliandolo (Universite Pierre et Marie Curie)

8 Quantum first detection time

We investigate the quantum first detection problem for a quantum walk using projective measurement postulates. A simple relation between the measurement free state function |psi> and |phi>_n is obtained, the latter is the first detection amplitude at the n-th attempt. This relation is the quantum renewal equation, its classical counter part is widely used to find statistics of first passage time for random walks and Brownian motion. We investigate statistics of first detection for open and closed systems (first arrival or passage is not well defined in quantum theory). For closed systems, like a ring, with a translation invariant Hamiltonian, we find Zeno physics, optimum sampling times, critical sampling effect related to revivals, dark states, and quantisation of the mean detection time. For a quantum walk on the line, with particle starting on |x_i> and detected on the origing |0>, with a tight-binding Hamiltonian with hops to nearest neighbours, we find the detection probability decays like (time)^(-3) with super imposed quantum oscillation, thus the quantum exponent is double its classical counter part. The Polya problem is discussed, and it is found that in one dimension the total detection probability, does not depend on the initial distance of the particle from detector, though survival of the particle is not unity. There is an optimal sampling time which maximises the total detection probability. $ $ Joint work with Harel Fridman, David Kessler, and Felix Thiel.

Speaker: Eli Barkai (Bar-Ilan University, Israel)

9 Mesoscopic and metastable quantum systems

We shortly review the transient dynamics of mesoscopic systems, such as Josephson junctions, in noisy environments. The role of noise induced solitons and breathers on the mean switching time from the superconducting metastable state to the resistive state, in the presence of an external noise source modeled by α-stable Lévy distributions, will be outlined. Thereafter, the dissipative dynamics of a particle moving in a strongly asymmetric double well potential, interacting with a thermal bath will be considered. Common wisdom is that quantum fluctuations enhance the escape rate from metastable states in the presence of dissipation. We show that dissipation can enhance the stability of a quantum metastable system. We find that the escape time from the metastable region has a nonmonotonic behavior, with a maximum, versus the system-bath coupling, and with a minimum versus the temperature, thus producing a stabilizing effect. Therefore, as the temperature increases, an enhancement of the escape time is observed, increasing the stability of the metastable state. These results shed new light on the role of the environmental fluctuations in stabilizing quantum metastable systems. We will show then, how the combined effects of strong Ohmic dissipation and monochromatic driving affect the stability of a quantum system with a metastable state. We find that, by increasing the coupling with the environment, the escape time makes a transition from a regime in which it is substantially controlled by the driving, displaying resonant peaks and dips, to a regime of frequency-independent escape time with a peak followed by a steep fall off. The quantum noise enhanced stability phenomenon is observed in the system investigated. Resonant activation, the presence of a minimum in the mean escape time, occurs when the time scale of the modulations is the same as the characteristic time scale of the system’s dynamics. The simple quantum system considered displays as well the general features that at slow modulations the mean escape time is dominated by the slowest configuration assumed by he system, while at fast modulations the escape dynamics is determined by the average configuration. $ $ [1] D. Valenti, C. Guarcello, and B. Spagnolo, Phys. Rev. B **89**, 214510 (2014). [2] C. Guarcello, D. Valenti, and B. Spagnolo, Phys. Rev. B **92**, 174519 (2015). [3] C. Guarcello, D. Valenti, B. Spagnolo, V. Pierro and G. Filatrella, Nanotechnology, **28**, 134001 (2017). [4] D. Valenti, L. Magazzù, P. Caldara, and B. Spagnolo, “Stabilization of quantum metastable states by dissipation”, Physical Review B **91**, 235412 (7) (2015). [5] Luca Magazzù, Angelo Carollo, Bernardo Spagnolo, Davide Valenti, “Quantum dissipative dynamics of a bistable system in the sub-Ohmic to super-Ohmic regime”, Journal of Statistical Mechanics: Theory and Experiment 054016 (2016). [6] B. Spagnolo, C. Guarcello, L. Magazzù, A. Carollo, D. Persano Adorno, D. Valenti, “Nonlinear Relaxation Phenomena in Metastable Condensed Matter Systems”, Entropy, 19 (1), 20 (2017).
 [7] L. Magazzù, P. Hänggi, B. Spagnolo, and D. Valenti, “Quantum Resonant Activation”, Physical Review E 95 (13), 042104 (2017).

Speaker: Bernardo Spagnolo (University of Palermo)

Session 2: Panel B

Convener: Prof. Robert Holyst (Institute of Physical Chemistry PAS)

10 A tribute to Marian Smoluchowski's legacy on colloid type matter aggregation, and related issues

In 1916 Marian Smoluchowski proposed a case of constant-kernel cluster cluster aggregation, for which it is manageable to find analitycally by employing scaling arguments, a solution in terms of the cluster size (k) distribution function, n(k) [1,2]. By applying this scaling function it is then possible to get, within the long times' limit, the results for the mean cluster size {k} and the total number of the clusters N, both scalable in terms of time t with a single exponent, g [2]. The clustering arguments, first introduced by Smoluchowski [1], are easily applicable to statistical description of physical-metallurgical processes and ceramic-polycrystalline evolutions, termed the normal grain growth, in which bigger clusters grow at the expense of their smaller neighboring counterparts due to capillary conditions [3]. The normal grain growth, and its dynamics, can be expressed in d-dimensional space (d - Euclidean dimension of the space). Upon identifying {k} from the Smoluchowski description with {R}, the mean cluster radius' size from the normal grain growth approach, and by taking the "extreme" condition of k >> 0, one is able to embark on their equivalence by stating rigorously that g=1/(d+1), since the asymptotic scaling rule for N (here: the number of grains) goes via a simple logarithmic depiction as: ln[N]~-ln[g]. The crucial assumption, however, that assures the equivalence claimed, appears to be fully feasible when rearranging the time domain by substituting t in a way such that a new rescaled time variable T(t) is given by a definite integral in [0,t] upon dT(t)=dt/f(t), with an adjustable function f, coming from the dispersive or long-tail, or fractal kinetics' arguments [4]. The arguments may at least qualitatively concern biomembranes dynamics; they can also contribute to nucleation-growth processes in (psychodynamic-clustering) living matter conditions [5-7]. $ $ [1] M. von Smoluchowski, Physikalische Zeitschrift **17**, 585 (1916). [2] R. Jullien, Croatica Chemica Acta **65**(2), pp. 215-235 (1992). [3] P.A. Mulheran, J.H. Harding, Materials Science Forum **94-96**, pp. 367-372, 1992. [4] A. Plonka, Dispersive Kinetics, Kluwer, Dordrecht, 2002. [5] A. Gadomski, A. Gadomski, European Physical Journal B **9**, 569 - 571 (1999). [6] A. Gadomski, M. Ausloos, T. Casey, Nonlinear Dynamics in Psychology & Life Sciences **21**/2, 129-141 (2017). [7] A. Gadomski, Philosophical Magazine Letters **70**, 335 (1994).

Speaker: Adam Gadomski (UTP University of Science and Technology Bydgoszcz, Poland)

11 Stationary diffusion among partially reactive sinks: from von Smoluchowski to recent advances

In 1917, von Smoluchowski founded the first mathematical theory of diffusion-limited reactions by computing the diffusive flux towards a perfect spherical sink. In spite of many advances over the past hundred years, stationary diffusion in complex media with numerous sinks of various shapes and reactivities remains poorly understood. After a brief overview, we present a recently developed generalized method of separation of variables (GMSV) to solve boundary value problems for the Poisson equation in three-dimensional canonical domains (e.g., parallelepipeds, cylinders, spheres, spheroids, ..., and their combinations). In particular, we derive a semi-analytical representation of the Green function for an arbitrary configuration of non-overlapping partially reactive spherical sinks. This is the key object to determine various characteristics of stationary diffusion such as reaction rate, escape probability, harmonic measure, residence time, and mean first passage time, to name but a few. Based on this solution, we introduce and investigate an effective reaction radius of individual sinks or their clusters that significantly generalizes the famous Smoluchowski formula by accounting for diffusion interactions between sinks and their mutual screening.

Speaker: Denis Grebenkov (CNRS)

12 Stochastic advection-reaction-diffusion model for phytoplankton populations in a 2D spatial domain

Phytoplankton lies at the base of the food chain of seas and oceans, and it is responsible for about 80% of the total *chlorophyll a*. As a consequence, phytoplankton determines the trophic structures of marine ecosystems, while influencing the total abundance and the spatial distributions of marine biological species, e.g. fish populations. Thus the study of spatio-temporal dynamics of phytoplankton populations and the development of models which predict the trend of primary production become of paramount importance to understand and forecast the dynamics of biological species within marine ecosystems. Here it is presented a two-dimensional advection-reaction-diffusion model to describe the dynamics of four phytoplankton populations in a real ecosystem located in the Channel of Sicily (South Mediterranean Sea). Light intensity and nutrient concentration represent the limiting factors for the phytoplankton growth. Specifically, due to the characteristics of the marine ecosystem analyzed, i.e. a transect consisting of twelve marine stations between Cape Passero (Sicily) and Misurata (Libya) [1], the limiting nutrient component is phosphorus. Phytoplankton abundances are first obtained by solving numerically a system of deterministic partial differential equations and then converted *chlorophyll a* concentrations [2], whose spatial distributions are compared with those obtained from field data collected in the twelve marine stations [3]. Statistical checks based on the chi-square test indicate a good agreement between theoretical and experimental distributions of *chlorophyll a* concentration. Deterministic models however can not fully describe the nonlinear dynamics of a real ecosystem continuously exposed not only to deterministic but also to random perturbations coming from the environment. To take into account the random fluctuations of the environmental variables, the deterministic model is modified by inserting in the equations Gaussian noise sources [4]. As confirmed by checks based on the chi-square test, the distributions of *chlorophyll a* concentration obtained by the stochastic model fit the field data better than those calculated by the deterministic model. It is worth noting that in this study real values for physical and biological variables were used. Specifically, the analysis exploits hydrological and nutrients data acquired in situ, including intraspecific competition for limiting factors. The study and the results discussed here indicate the effectiveness of this approach for reproducing real spatial distributions of *chlorophyll a* concentration. Moreover we note that the stochastic advection-reaction-diffusion model presented in this work can be extended to different marine ecosystems and used as a global model to forecast eventual decreases in the abundance of primary production and to prevent the consequent decline of fish species. $ $ [1] F. Placenti, K. Schroeder, A. Bonanno, S. Zgozi, M. Sprovieri, M. Borghini , P. Rumolo, G. Cerrati, S. Bonomo, S. Genovese, G. Basilone, D. A. Haddoud, B. Patti, A. El Turki, M. Hamza, S. Mazzola, Water masses and nutrient distribution in the Gulf of Syrte and between Sicily and Libya, J. Mar. Syst. 121-122, 36-46 (2013). [2] C. Brunet, R. Casotti, V. Vantrepotte, F. Conversano, Vertical variability and diel dynamics of picophytoplankton in the Strait of Sicily, Mediterranean Sea, in summer, Mar. Ecol. Prog. Ser. 346, 15-26 (2007). [3] D. Valenti, G. Denaro, R. Ferreri, S. Genovese, S. Aronica, S. Mazzola, A. Bonanno, G. Basilone, B. Spagnolo, Sci. Rep., Spatio-temporal dynamics of a planktonic system and chlorophyll distribution in a 2D spatial domain: matching model and data 7, 220 (2017). [4] G. Denaro, D. Valenti, B. Spagnolo, G. Basilone, S. Mazzola, S. W. Zgozi, S. Aronica, A. Bonanno, Dynamics of two pico-phytoplankton groups in Mediterranean Sea: Analysis of the deep chlorophyll maximum by a stochastic advection-reaction-diffusion model, PLoS ONE 8, e66765 (2013).

Speaker: Davide Valenti (Department of Physics and Chemistry, University of Palermo)

13 Thermodynamic activation energy for self diffusion and order-order relaxation in intermetallic compounds: atomistic model and Monte Carlo simulations

Self-diffusion and the ‘order order’ relaxation process in intermetallic compounds is described in terms of effective atomic jump frequencies and the current degree of chemical long-range order. It is demonstrated that the thermodynamic activation energies of self-diffusion and the ‘order-order’ relaxation can be expressed in terms of the activation energies of more elementary processes. As the derived expressions differ from each other, the values of the thermodynamic activation energies for self-diffusion and the ‘order order’ relaxation can be different although both processes are controlled by the same vacancy-mediated elementary atomic jumps. In order to assess the the validity of the derived formulae different B2-ordering binary systems are simulated. The results of the computer experiments are in good agreement with the tested formulae. It is shown that the relationship between the activation energies observed in triple defect B2-ordering binaries, where the value of the activation energy for order-order relaxations is substantially lower than that for self-diffusion, does not hold in the case of non-triple-defect binaries. Using the tested formulae, the origin of the effect is elucidated and attributed to the atomistic origin of the tendency for triple-defect disordering. $ $ P. Sowa, A. Biborski, M. Kozłowski, R. Kozubski, I.V. Belova, G.E. Murch: Atomistic origin of the thermodynamic activation energy for self diffusion and order-order relaxation in intermetallic compounds. Part I and Part II, Philos.Mag., **97**, 1361-1374, 1375-1397 (2017).

Speaker: Rafal Abdank-Kozubski (M. Smoluchowski Institute of Physics, Jagiellonian University in Krakow)

Session 2: Panel C

Convener: Prof. Zbigniew Grzywna (Silesian University of Technology, Faculty of Chemistry)

14 Transient anomalous diffusion in ratchet systems

Anomalous diffusion can be detected in various systems. We show that anomalous diffusion may emerge in a straightforward, one dimensional classical nonequilibrium dynamics of a Brownian particle moving in a ratchet potential and driven by both an unbiased time-periodic force and thermal fluctuations of Gaussian nature. In a tailored parameter regime for which the deterministic counterpart of the system is non-chaotic, the mean square deviation of the Brownian particle coordinate evolves in three following stages: initially as superdiffusion, next as subdiffusion and finally as normal diffusion in the asymptotic long time limit. The lifetimes of superdiffusion and subdiffusion can be controlled by system parameters and can last many many orders longer than characteristic times of the system, thus being comfortably detectable experimentally. The findings are distinct from existing knowledge and suggest reconsideration of generally accepted opinion that anomalies are due to large and rare fluctuations that are characterized by broad distributions with power- law tails. We explain the underlying mechanism standing behind the emergence of diffusion anomalies and control of their regimes which are related to ergodicity of the system and ultraslow relaxation of the particle velocity towards its non- equilibrium stationary state.

Speaker: Jerzy Luczka (University of Silesia)

15 Temperature-abnormal diffusivity and weak ergodicity breaking in space-periodic systems driven by external forces

The phenomena of diffusion over a potential energy landscape play a key role in a number of processes in physics, chemistry and biology. In this talk a set of original theoretical results on diffusion enhancement of underdamped Brownian particles in symmetric space-periodic potential due to external forcing is presented [1-5]. We demonstrate that depending on the value of the constant external force in underdamped space-periodic systems dfferent functional dependences of the diffusivity on the temperature are realized. It is shown by numeric simulations of the Langevin equation that the phenomenon of diffusivity growth with the temperature decreasing (“temperature-abnormal diffusivity”- TAD) is manifested in a narrow interval of applied external forcing. We demonstrate that weak ergodicity breaking takes place in TAD region. The correlation time tends to infinity as ~exp(+U/kBT) at T→0 in TAD region. It is well-known that the double-well system is a typical classical memory device. We show that particle dynamics in underdamped space periodic systems may be considered as overdamped particle movement in effective double-well velocity space potential. Based on the double-well model the analytical expression for diffusion coefficients in TAD region is derived. The functional dependence of TAD region width and its position on the friction coefficient and system parameters is found. These results allow for simple experimental verification, and have practical applications -- in physics of adsorbates, diffusion of interstitials, nanoparticle sorting, hydrogen energetics to name a few. $ $ [1] I. G. Marchenko, I. I. Marchenko, Europhys. Let. 100, 50005 (2012). [2] I. G. Marchenko, I. I. Marchenko, A. V. Zhiglo, Euro. Phys. Journ. B87, 10 (2014). [3] I. G. Marchenko, I. I. Marchenko, JETP Lett., 95 (2012) 137. [4] I. G. Marchenko, I. I. Marchenko, Journ. of Phys. Conf. Ser. 514, 012045 (2014). [5] I. G. Marchenko, I. I. Marchenko, A. V. Zhiglo, arXiv:1701.01424v2 (2017).

Speaker: Ivan Marchenko (National Scientific Centre “Kharkov Institute of Physics and Technology”)

16 Time-dependent fluctuations and superdiffusivity in the driven lattice Lorentz gas

We consider a tracer particle on a lattice in the presence of immobile obstacles. Starting from equilibrium, a force pulling on the particle is switched on, driving the system to a new stationary state. We solve for the complete transient dynamics of the fluctuations of the tracer position along the direction of the force. The analytic result, exact in first order of the obstacle density and for arbitrarily strong driving, is compared to stochastic simulations. Upon strong driving, the fluctuations grow superdiffusively for intermediate times; however, they always become diffusive in the stationary state. The diffusion constant is nonanalytic for small driving and is enhanced by orders of magnitude by increasing the force.

Speaker: Thomas Franosch (Universität Innsbruck)

17 Variational formula for the current generating function and finite-time thermodynamic uncertainty relations

Bounds on the current generating function for stochastic dynamics and the thermodynamic uncertainty relations that follow from them have recently attracted much attention. Here, we focus on the space-time continuous case of Langevin dynamics. We derive a variational formula for the generating function of a generalized current, which is valid at finite time, extending the previously known results for the long-time limit. We show that the proof of the recently proposed finite-time thermodynamic uncertainty relation follows from the variational formula in a straightforward way. This relation provides a universal bound on any current in a non-equilibrium steady state in terms of the entropy production. We also discuss possible extensions to the transient case and to systems with time-dependent driving.

Speaker: Andreas Dechant (Kyoto University)

16:00 Coffee Break

Session 3: Panel A

Convener: Dr Bartłomiej Dybiec (IF UJ)

18 Progressive quenching

We will describe the basic idea and some applications of the processes when the system's degrees of freedom are progressively quenched. This work has been done in collaboration with Bruno Ventejou and Michael Etienne (paper in preparation).

Speaker: Ken Sekimoto (Univ. Paris-Diderot & ESPCI)

19 Foundations of the local equilibrium concept

Local equilibrium states change slowly in time because they are almost stationary. As a consequence local equilibrium states have to be related to local states that are time-invariant. It has been argued in the literature that a proper mathematical formulation of local equilibrium states must start from the class of time-invariant measures for infinitely extended systems [1]. This presentation argues that the set of time-invariant measures of infinite systems is too small [2]. A suitable extension are states of bounded mean oscillation (BMO-states) that are also close to time-invariant states. BMO-states are states for which the expectation values of all observables are functions of bounded mean oscillation in time. Results for long time scaling limits of induced time flows on subsets of BMO-states then provide the mathematical foundation for the local equilibrium concept. $ $ [1] H. Spohn, Large Scale Dynamics of Interacting Particles, 1991 [2] R. Hilfer, Analysis, 36, 49-64 (2016)

Speaker: Rudolf Hilfer (Universitaet Stuttgart)

20 Fluctuating hydrodynamics of one-dimensional nonlinear chains

One-dimensional particle systems are known to be anomalous with respect to the dynamics of their hydrodynamic conserved fields and their related currents. We review some of the predictions of mode-mode coupling theory combined with exact results by Prähofer and Spohn [J. Stat. Phys., vol. 115, 255 (2004)] to derive asymptotic expressions for the time-correlation functions of the hydrodynamic modes and their currents. These results are compared to extensive computer simulations for two simple fluids with non-linear short-range interactions.

Speaker: Harald Posch (University of Vienna)

Session 3: Panel B

Convener: Prof. Aleksander Weron (Hugo Steinhaus Center, Faculty of Pure and Applied Mathematics, Politechnika Wrocławska)

21 Harmonic spectral components in time sequences of Markov correlated events with an application to EEG and MEG signals

The talk is addressed to the analysis of time sequences of Markov correlated events give rise to a line power spectrum having a relevant physical interest. In particular, Markov matrices able to represent closed loop sequences of events with arbitrary distribution, generated in a steady physical condition, generate a large set of line spectra, covering a very broad frequency range. The spectral lines is given by a matrix equation based on a generalized Markov matrix involving the Fourier transform of the distribution functions representing the time intervals between successive events of the sequence. The theoretical power spectra is then applied to describe the emergence of a broad set of waves found in the electro and magneto-encephalograms, whose frequency ranges from 0.5 to about 40 Hz, in terms of the effects produced by chains of firing neurons within the complex neural network of the brain. Synchronized closed loop sequences of firing neurons are considered and a few numerical simulations are reported.

Speaker: Anna Carbone (Politecnico di Torino)

22 Characterizing rare fluctuations in soft particulate flows

Soft particulate media include a wide range of systems involving athermal dissipative particles both in non-living and biological materials. Characterization of flows of particulate media is of great practical and theoretical importance. A fascinating feature of these systems is the existence of a critical rigidity transition in the dense regime dominated by highly intermittent fluctuations that severely affects the flow properties. Here, we unveil the underlying mechanisms of rare fluctuations in soft particulate flows. We find that rare fluctuations have different origins above and below the critical jamming density and become suppressed near the jamming transition. We then conjecture a time-independent local FR, which we verify numerically, and that gives rise to an effective temperature. We discuss similarities and differences between our proposed effective temperature with the conventional kinetic temperature in the system by means of a universal scaling collapse.

Speaker: S. H. E. Rahbari (KIAS)

23 Glass transition as the consequence of spatially correlated stochastic dynamics

Despite the decades of intense research, the glass transition, i.e. the extreme rise in the viscosity (by $10^{14}$ for molecular and $10^3$ for colloidal glasses) of the disordered system as it becomes denser/colder, is far from being fully understood. One important limitation here is the lack of analytically solvable models for the systems with arbitrary interactions. In this presentation such one-dimensional model is introduced. The model originates from the recent theoretical advancements in the field of Langevin dynamics driven by the spatially correlated noise (SCN). SCN can be linked to the diffusion in colloids or dynamic heterogeneity in molecular systems. Recently, it has been shown that the thermodynamic consistency requires SCN to be accompanied by the dissipation represented as the friction-response matrix. I will show that in the thermodynamic limit, this matrix can develop a genuine singularity in dissipation for finite volume packing, thus heralding the system jamming. Since this happens under the assumption of complete molecular disorder, this jamming is identified as the glass transition. The model introduces new perspective on the role of spatial correlations in vitrification, i.e. it shows that they might not be the consequence, but the cause of jamming. It also provides the exact relation between the noise correlation length and the critical packing. Finally, it suggests that the spectrum of the friction-response matrix might be the order parameter for the glass transition.

Speaker: Maciej Majka (Jagiellonian University)

24 Long range correlations in dynamical systems and in observed data

Long range temporal correlations (LRC) in noise-like signals can be detected through the scaling behaviour of the mean squared displacement (MSD) of the pathes which one obtains by integrating over the signal. Detrended fluctuation analysis has become a standard tool which beyond a simple MSD analysis is able to remove the effects of trends on the signal. In the first part of this talk we present a sketch of theoretical considerations which give a better justification for DFA than it has been presented before. In the second part, we show the consequences of LRC on the convergence of time averages, on the probability for large deviations, and for the estimation of trends. In order to transfer these findings to real world data, we need paradigmatic data models with a minimum of free parameters.

Speaker: Holger Kantz (Max Planck Institute for the Physics of Complex Systems)

Session 3: Panel C

Convener: Prof. Maciej A. Nowak (Jagiellonian University)

25 Dynamical maps on quantum Orlicz spaces

We present a new rigorous approach based on Orlicz spaces for the description of the statistics of large regular statistical systems, both classical and quantum. We emphasize that the presented formalism is applicable to QFT! The pair of Orlicz spaces we explicitly use are respectively built on the exponential function (for the description of regular observables) and on an entropic type function (for the corresponding states). They form a dual pair (both for classical and quantum systems). This pair $\langle L^{\cosh - 1}, L\log(L+1)\rangle$ has the advantage of being general enough to encompass regular observables, and specific enough for the latter Orlicz space to select states with a well-defined entropy function. Quantum dynamical maps are defined and studied for quantum statistical physics based on Orlicz spaces. We show that even in the most general non-commutative contexts, completely positive Markov maps satisfying a natural Detailed Balance condition, canonically admit an action on a large class of quantum Orlicz spaces. This is achieved by the development of a new interpolation technique, specifically suited to the above context, for extending the action of such maps to the appropriate intermediate spaces of the pair $\langle L^\infty,L^1\rangle$.

Speaker: Wladyslaw Adam Majewski (The Gdansk University)

26 Where are we with the understanding of a collective dynamics of quasi-periodically perturbed particles?

Marian Smoluchowski provided an explanation of the Brownian motion of particles. The equation for a particle's displacement in space that he proposed in 1906 provided an important basis for the theory of stochastic processes. This initiated the whole new field of stochastic dynamics that blossomed during the last century. In this talk we will discuss what happens to the particles if external deterministic forces are continuously imposed on them, and how a collective dynamics emerges to describe particles under external forcing. $ $ The time-varying, non-autonomous, dynamics that emerges under external forcing has been detected in living, as well as man-made, systems. Currently, however, non-autonomous dynamics is commonly considered easy to deal with - either by transforming it into autonomous dynamics, for which an abundance of tractable analytic tools is available, or by considering it as belonging to the class of stochastic systems where, again, numerous analytic approaches exist. $ $ In the talk, we will argue that there is a need for a theory of a new class of non-autonomous systems with time-varying dynamics due to external forcing. We will first present examples of non-autonomous dynamics measured from biological cells, the cardiovascular system and the brain, as well as from experiments with electrons on the surface of liquid helium. $ $ Then, we will review briefly the existing numerical methods for the detection and analysis of non-autonomous dynamics from data. In the third part of the talk, we will summarise our current work on non-autonomous dynamics when the external perturbation is of quasi-periodic origin, arguing that most of the challenging problems still remain unsolved and that our better understanding of non-autonomous, finite-time dynamics could make a similarly significant contribution to that of Smoluchowski more than 100 years ago, thereby advancing our understanding of nature in general. $ $ Y Shiogai, A Stefanovska, PVE McClintock, Nonlinear dynamics of cardiovascular ageing, Phys. Rep. **488**: 51-110, 2010 YF Suprunenko, PT Clemson, A Stefanovska, Chronotaxic systems: A new class of self-sustained nonautonomous oscillators, Phys. Rev. Lett. **111**: 024101, 2013 PT Clemson, A Stefanovska, Discerning non-autonomous dynamics, Phys. Rep. **542*: 297-368, 2014 P Clemson, G Lancaster, A Stefanovska, Reconstructing time-dependent dynamics, Proc. IEEE 104: 223-241, 2016 T Stankovski, T Pereira, PVE McClintock, A Stefanovska, Coupling functions: Universal insights into dynamical interaction mechanisms, Rev. Mod. Phys. in press, 2017

Speaker: Aneta Stefanovska (Physics Department, Lancaster University)

27 Aerated Poisson distributions and their exact approximants.

We analyze the properties of combinatorial numbers appearing in the normal ordering of powers of certain differential operators. They are natural generalizations of the conventional Bell numbers. We explicitly construct the solutions of the Stieltjes moment problems with these combinatorial sequences. It turns out that in certain cases one encounters as solutions the discrete probability distributions based on lacunary subsets of positive integers. They generalize the standard Poisson laws and are called aerated Poisson distributions. We furnish explicit approximants of the aerated Poisson distributions through continuous functions via reparametrization of auxiliary solutions for other generalized Bell numbers.

Speaker: Prof. Karol Penson (University Paris 6)

18:30 Get Together Party

Tuesday, 5 September

Session 4: Panel A

Convener: Prof. Katja Lindenberg (University of California San Diego)

28 Intermediate asymptotics and aging phenomena in anomalous transport by flows.

Anomalous transport in flows is often invoked in discussion of anomalous transport phenomena as described by continuous-time random walk (CTRW) or Levy walk (LW) schemes. The first model describes the particles' transport in eddy lattices, and the model of a Levy walk interrupted by rests describes the transport in flows which consist of eddies and jets. The models adequately describe the intermediate-time dynamics of the mean squared displacement (MSD) of the transported particles from their initial positions under initial conditions corresponding starting on the separatrix between two eddies or between an eddy and a jet, and the long-time dynamics for any initial condition, when the initial conditions are already forgotten. $ $ Both random walk models lead to non-stationary dynamics on intermediate times, and exhibit aging phenomena. It is sometimes assumed that the corresponding models also can describe aging in flows. The aging phenomena in random walk schemes are connected with the walker's behavior during the very first step after the beginning of the observation, and assume that this dynamics is trivial (being at rest in CTRW, or either being at rest or moving along straight line in the interrupted LW) while the dynamics during the capturing periods in a flow is essentially quite complex and corresponds to rotations around elliptic points of eddies or oscillations in jets. $ $ We concentrate on the MSD of the transported particles from their initial positions, and discuss in detail the aging dynamics of MSD in flows. We show that the time-evolution of the MSD depends strongly on initial conditions, that simple CTRW / LW-dynamics only describes the intermediate-time behavior of the initial conditions discussed above, and that several other regimes (including superdiffusion or oscillations) are possible. Even in the case when simplified models correctly describe the intermediate time behavior of MSD when starting on the separatrix, they fail to describe the aging behavior of the MSD even in this case. We give the theoretical discussion of all theses issues, and illustrate our points by results of massive numerical simulations of the system.

Speaker: Igor Sokolov (Humboldt University Berlin)

29 Aging transient superdiffusive dynamics in in vivo neuronal mRNP transport: a Levy walk description

Localization of messenger ribonucleoproteins (mRNPs) plays an essential role in the regulation of gene expression required for long-term memory formation and neuronal development. Knowledge concerning the nature of neuronal mRNP transport is thus crucial for understanding how mRNPs are delivered to their target synapses. In this talk, we show experimental and theoretical evidence that the active transport dynamics of neuronal mRNPs, which is distinct from the previously reported motor-driven transport, follows an aging Levy walk. Such nonergodic, transient superdiffusion occurs because of two competing dynamic phases: the motor-involved ballistic run and static localization of mRNPs. Our proposed Levy walk model reproduces the experimentally extracted key dynamic characteristics of mRNPs with quantitative accuracy. Moreover, the aging status of the mRNP particles in an experiment is inferred from the model. The potential physical mechanisms for the observed aging behaviors are shortly discussed.

Speaker: Jae Hyung Jeon (Department of Physics, Pohang University of Science and Technology(POSTECH))

30 Anomalous diffusion, ageing, and non-errodicity

In 1905 Einstein formulated the laws of diffusion, and in 1908 Perrin published his Nobel-prize winning studies determining Avogadro's number from diffusion measurements. With similar, more refined techniques the diffusion behaviour in complex systems such as the motion of tracer particles in living biological cells is nowadays measured with high precision. Often the diffusion turns out to deviate from Einstein's laws. This talk will discuss the basic mechanisms leading to anomalous diffusion as well as point out the physical consequences. In particular the unconventional behaviour of non-ergodic, ageing systems will be discussed within the framework of different stochastic processes. Concrete examples include granular gases, biological cells, lipid membranes, and interacting many particle systems.

Speaker: Ralf Metzler (University of Potsdam)

Session 4: Panel B

Convener: Dr Lukasz Machura (University of Silesia)

31 Induced motion of a probe in contact with a nonequilibrium medium

We discuss how contact with a nonequilibrium bath can modify the effective dynamics of a probe. In particular, systematic forces may become nongradient; the second fluctuation-dissipation relation can be broken and the noise may be nonGaussian and showing power law distributed jumps.

Speaker: Christian Maes (KU Leuven)

32 How to measure load-dependent kinetics of individual motor molecules without a force-clamp

Molecular motors are responsible for numerous cellular processes from cargo transport to heart contraction. Their interactions with other cellular components are often transient and exhibit kinetics that depend on load. Here, we measure such interactions using a new method, “Harmonic Force Spectroscopy.” In this method, harmonic oscillation of the sample stage of a laser trap immediately, automatically and randomly applies sinusoidally varying loads to a single motor molecule interacting with a single track along which it moves. The experimental protocol and the data analysis are simple, fast and efficient. The protocol accumulates statistics fast enough to deliver single-molecule results from single-molecule experiments. We demonstrate the method’s performance by measuring the force-dependent kinetics of individual human beta-cardiac myosin molecules interacting with an actin filament at physiological ATP concentration. We show that a molecule’s ADP release rate depends exponentially on the applied load. This points to Kramer’s Brownian diffusion model of chemical reactions as explanation why muscle contracts with a velocity inversely proportional to external load.

Speaker: Henrik Flyvbjerg (Department of Micro- and Nanotechnology, Technical University of Denmark, Kongens Lyngby, Denmark)

33 Modelling heart rhytm variability in heart transplant patients by cellular automata on complex networks

In patients with end-stage heart disease the heart transplantation (HTx) is associated with significant improvement in survival and in quality of life. However strong immunosuppressive drugs together with processes of aging could lead to vasculopathy and fibrosis of the donor heart. Moreover a spontaneous process of reinnervation proceeds in the myocardial tissue. All together impact on progressive alternations in the myocardial structure what influence propagation of activation wave fronts. A variety of arrhythmias – abnormal heart rhythm, may occur which adversely affect the patient long term survival. $ $ Cellular automata modeling of signal propagation in the atrial muscle tissue is a rational compromise in resolving of physiological complexity, justified by efficiency in reproducing details of myocardial architecture. Consequently this modeling may explain key relationships between heart muscle structure and the propagation of activation wave fronts, possible reasons for the risk of arrhythmia. $ $ Combining our proposition for stochastic network cellular automata model of the human pacemaker [1] and 2D cellular automata model of fibrosis in atria proposed in [2], we investigate which changes in myocardial structure affects propagation of cell-to-cell signals to contract in such way that we observe abnormal heart rhythm. 24-hour Holter measurement, a noninvasive and cheap ECG recording provides information on erratic rhythms of HTx patients. By modeling of structural alternates in the heart tissue we reproduce properties of some individual HTx patient heart rhythm [3]. $ $ References 1. D. Makowiec Acta Phys.Pol.B Proc.Suppl. 7(2014) 347 2. K. Christensen et al, Phys. Rev. Lett. 114 (2015) 028104 3. D. Makowiec et al, Chaos, Solitons & Fractals 90 (2016) 101

Speaker: Danuta Makowiec (Institute of Theoretical Physics and Astrophysics, University of Gdansk)

Session 4: Panel C

Convener: Dr Maciej Majka (Jagiellonian University)

34 Nonergodic dynamics in the plasma membrane of living cells

Tracking individual proteins on the surface of live mammalian cells reveals complex dynamics involving anomalous diffusion and clustering into nanoscale domains. Theoretical models show that anomalous subdiffusion can be caused by different processes. Here we study the nonergodic dynamics of voltage gated ion channels in human embryonic kidney (HEK) cells and in hippocampal neurons. We perform time series and ensemble analysis of extensive single-molecule tracking. We show that in HEK cells, weak ergodicity breaking is found to be maintained by immobilization events that take place when the proteins are captured within clathrin-coated pits. However, in hippocampal neurons, ergodicity breaking is caused by transient confinement into nanoclusters with a 230-nm mean diameter. Ergodicity breaking in these cells is manifested in two different ways. First, significant differences are observed between time- and ensemble-averaged mean square displacements. Second, a dynamical functional test unmasks ergodicity breaking at the individual trajectory level.

Speaker: Diego Krapf (Colorado State University)

35 Isothermal Langevin dynamics in systems with power-law spatially dependent friction

We study the dynamics of Brownian particles in a heterogeneous one-dimensional medium with a spatially-dependent diffusion coefficient of the form $D(x)\sim|x|^c$, at constant temperature. The particle’s probability distribution function (PDF) is calculated both analytically, by solving Fick’s diffusion equation, and from numerical simulations of the underdamped Langevin equation. At large times, the PDFs calculated by both approaches yield identical results, corresponding to subdiffusion for $c < 0$, and superdiffusion for $0 < c < 1$. For $c > 1$, the diffusion equation predicts that the particles accelerate. Here, we show that this phenomenon, previously considered in several works as an illustration for the possible dramatic effects of spatially-dependent thermal noise, is unphysical. We argue that in an isothermal medium, the motion cannot exceed the ballistic limit ($\langle x2\rangle∼ t^2$). The ballistic limit is reached when the friction coefficient drops sufficiently fast at large distances from the origin, and is correctly captured by Langevin’s equation. $ $ [1] S. Regev, N. Gronbech-Jensen, and O. Farago, Phys Rev. E **94**, 012116 (2016).

Speaker: Oded Farago (Ben Gurion University)

36 Large deviations of surface height in the Kardar-Parisi-Zhang equation

The Kardar-Parisi-Zhang (KPZ) equation describes an important universality class of nonequilibrium stochastic growth. There has been much recent interest in the one-point probability distribution P(H,t) of height H of the evolving interface at time t. I will show how one can use the optimal fluctuation method (also known as the instanton method, the weak-noise theory, the macroscopic fluctuation theory, or simply WKB) to evaluate P(H,t) for different initial conditions in 1+1 dimensions. At short times the body of the height distribution is Gaussian, but its tails are non-Gaussian and highly asymmetric. In a moving frame, one of the tails coincides, at all times, with the proper tail of the Tracy-Widom distribution (for the flat and curved interface), and of the Baik-Rains distribution (for the stationary interface). The other tail displays a behavior that differs from the known long-time asymptotic. At sufficiently large |H| this large-deviation tail also persists at arbitrary long times. The case of stationary interface is especially interesting. Here at short times the large deviation function of the height exhibits a singularity at a critical value of |H|. This singularity results from a symmetry-breaking of the "optimal path" of the system, and it has the character of a second-order phase transition.

Speaker: Baruch Meerson (Hebrew University of Jerusalem)

10:30 Coffee break

Session 5: Panel A

Convener: Prof. Miguel Rubi

37 Nonequilibrium steady states in Langevin thermal systems

Equilibrium is characterized by its fundamental properties such as the detailed balance, the fluctuation-dissipation relation, and no heat dissipation. Based on the stochastic thermodynamics, we show that these three properties are equivalent to each other in conventional Langevin thermal systems with microscopic reversibility. Thus, a conventional steady state has either all three properties (equilibrium) or none of them (nonequilibrium). In contrast, with velocity-dependent forces breaking the microscopic reversibility, we prove that the detailed balance and the fluctuationdissipation relation mutually exclude each other and no equivalence relation is possible between any two of the three properties. This implies that a steady state of Langevin systems with velocitydependent forces may maintain some equilibrium properties but not all of them. Our results are illustrated with a few example systems.

Speaker: Hyunggyu Park (Korea Institute for Advanced Study)

38 Brownian yet non-Gaussian Diffusion

A growing number of biological, soft, and active matter systems are observed to exhibit normal diffusive dynamics with a linear growth of the mean-squared displacement, yet with a non-Gaussian distribution of increments. Based on the Chubinsky-Slater idea of a diffusing diffusivity, we here establish and analyze a minimal model framework of diffusion processes with fluctuating diffusivity. In particular, we demonstrate the equivalence of the diffusing diffusivity process with a superstatistical approach with a distribution of diffusivities, at times shorter than the diffusivity correlation time. At longer times, a crossover to a Gaussian distribution with an effective diffusivity emerges. Specifically, we establish a subordination picture of Brownian but non-Gaussian diffusion processes, which can be used for a wide class of diffusivity fluctuation statistics. Our results are shown to be in excellent agreement with simulations and numerical evaluations. $ $ Aleksei V. Chechkin, Flavio Seno, Ralf Metzler, and Igor M. Sokolov, PHYSICAL REVIEW X 7, 021002 (2017).

Speaker: Aleksei Chechkin (Akhiezer Institute for Theoretical Physics)

39 Transport of granular materials in turbulent flows (or sand in streams)

The notion that the kinematics of sediment transported in streams is well-represented by quasi-random motions amenable to Smoluchowski-type diffusion was first proposed by Hans Albert Einstein at his renowned father’s suggestion. Since then, there have been attempts to adapt formalisms of diffusion and anomalous diffusion developed for thermodynamic systems to the start-and-stop and spatially variable behavior of sediment transport. New high-resolution measurements of sediment particle motions in laboratory flumes indicate that the mean squared displacement of tracer particles , when treated as a plume reflects a nonlinear increase in the variance in hop distances with increasing travel time. Ensemble calculations of MSD indicates a transition from correlated random walks to normal diffusion. Normal behavior also is reflected in the particle velocity autocorrelation function. Spatial variations in particle entrainment produce a flux from sites of high entrainment toward sites of low entrainment; thus, an entrainment form of flux and continuity equations are used for describing statistically expected transport behavior.

Speaker: Rina Schumer (Desert Research Institute)

Session 5: Panel B

Convener: Prof. Henrik Flyvbjerg (Technical University of Denmark)

40 A mesoscopic model for the DNA G-quadruplex stability analysis

The G-quadruplexes (G4) are non-canonical secondary DNA and RNA structures composed of four guanine basis bonded each other in a quartets forming piled planes. They have been found both in vivo and in vitro cultures, and have important role in telomere end-protection, and chromosome stability. Their folding patterns and structures are also found in eukaryotic promoter regions of oncogenes, making them increasingly recognized among chemists and biologists due to their potential applications in Nanomedicine as therapeutic targets in cancer treatments. $ $ In the last years, single-molecule techniques have attracted much attention between the scientific community and a number of groups have used it extensively to analyze the mechano-chemical behavior of DNA and RNA. Optical and magnetic tweezers, as well as Atomic Force Microscopies, are employed to characterize not only the mechanical stability and unfolding dynamics of G-quadruplexes, but also to unveil structural intermediates not accessible to ensemble-average techniques due to their relatively low occurrence. $ $ The stability of the G-quadruplex structure is related, among the others, to the specific structural G-quadruplex conformation, and the presence of a cation between each G4 planes. To date, many experiments have been conducted, which want to finely analyze rupture profiles in single force-extension curves. Although the increasing number of experiments on the subject, the theoretical predictions remain difficult, due essentially to the long computational time required by atomistic simulations, which, moreover, use parameter values (for example the velocity at which one extreme of the quadruplex is pulled to induce the rupture) some orders of magnitude far away from the experimental values. $ $ With the aim to bridge the gap between experiment and theoretical expectations, we build a mesoscopic physical model of the G-quadruplex structure with a reduced number of degrees of freedom and effective potential that permits to study the mechanical unfolding in a wider interval of time scales than those allowed in all atom simulations, in particular under different pulling velocities. The subsequent analysis on the light of the most recent stochastic theories for rupture force - as those of Bell, Dudko and Yoreo - permit the estimations of the potential barriers and positions that characterize the energy landscape of the unfolding process. $ $ Some validation of the model with the results of experiments will be presented.

Speaker: Alessandro Fiasconaro (Universidad de Zaragoza, Spain)

41 Diffusion of a tagged particle in two dimensional elastic networks

I will discuss the long time asymptotic behavior of a tagged particle in two dimensional systems, where the particles are stuck with their neighbors. This corresponds to single-file diffusion in one dimension, where the mean squared displacement of a particle grows with the square root of time. In two dimensions it turns out that the mean square displacement grows logarithmically. I will show how one can arrive at these results through an approach called harmonization.

Speaker: Michael Lomholt (University of Southern Denmark)

42 Stochastic gene expression in cells undergoing division

Stochasticity in gene expression is one of the most important problems of quantitative biology. It has been shown that, in the systems as small as living cells, production of proteins is strongly affected by random fluctuations coming from various sources. As a result, the biological noise is a meaningful factor influencing cellular processes and cell-fate decisions. The particular questions explored within the field of quantitative biology are, among others, the correct identification of noise sources and correct estimation of noise parameters, e.g., frequencies and sizes of the random bursts of protein production. We propose a stochastic model of gene expression in cells undergoing division. The model combines a deterministic approximation of protein degradation and the two sources of noise: 1) Random bursts of protein production, and 2) more or less random duration of the cell cycle. Random partitioning of proteins between daughter cells is also possible as the third source of noise. In the classical model proposed by the Xie group, the effect of cell division was tacitly identified with the effect protein degradation. We show that this may not be a correct assumption and the values of mean burst size and mean burst frequency inferred from the experiments using the classical model may be wrong. We show that our model provides more reasonable estimates for these quantities. Moreover, our model demonstrates that the “noise floor”, observed in the experiments and previously ascribed to an unidentified extrinsic noise, may be the effect of cell division. Our model sets physical constraints, based on the degree of randomness in cell cycle duration, for the levels of noise in gene expression.

Speaker: Anna Ochab-Marcinek (Institute of Physical Chemistry, Polish Academy of Sciences)

43 Mechanical interactions affect biological evolution in bacterial colonies

Bacterial conglomerates such as biofilms and microcolonies are ubiquitous in nature and play an important role in industry and medicine. In contrast to well-mixed cultures routinely used in microbial research, bacteria in a microcolony interact mechanically with one another and with the substrate to which they are attached. Here we use a computer model of a microbial colony of rod-shaped cells to investigate how physical interactions between cells determine their motion in the colony and how this affects biological evolution. We show that the probability that a faster-growing mutant ``surfs'' at the colony's frontier and creates a macroscopic sector depends on physical properties of cells (shape, elasticity, friction). Although all these factors contribute to the surfing probability in seemingly different ways, they all ultimately exhibit their effects by altering the roughness of the expanding frontier of the colony and the orientation of cells. Our predictions are confirmed by experiments in which we measure the surfing probability for colonies of different front roughness. Our results show that physical interactions between bacterial cells play an important role in biological evolution of new traits, and suggest that these interaction may be relevant to processes such as de novo evolution of antibiotic resistance.

Speaker: Bartlomiej Waclaw (University of Edinburgh)

Session 5: Panel C

Convener: Prof. Piotr Garbaczewski (University of Opole, Poland)

44 Quantum model of self-oscillations in chemical engines

A standard textbook picture of solar, thermoelectric and fuel cells based on a direct transformation of light, heat or chemical energy into a direct current (DC) contradicts the basic principles of electrodynamics and thermodynamics. The proposed solution of this problem involves a single oscillating degree of freedom called work reservoir (depository) or a piston, which executes self-oscillations fed by a constant energy supply. In the mentioned examples, it is a mode of plasma oscillations and the resulting charge oscillations are finally rectified to DC by a diode mechanism. The onset of self-oscillations is illustrated by a simple quantum Markovian model of a harmonic oscillator coupled to chemical reservoirs. The proper definition of work output is discussed in terms of ergotropy.

Speaker: Robert Alicki (University of Gdansk)

45 Order in quantum compass and orbital $e_g$ models

Exchange interactions in orbital models are frustrated even on a square lattice, where two $T=1/2$ pseudospin components $T_i^{\gamma}(\theta)$ parameterized by angle $\theta\in(0,\pi/2]$ interact by terms $JT_i^{\gamma}(\theta)T_j^{\gamma}(\theta)$. Maximal frustration in the quantum compass model with $T_i^{\gamma}(\pi/2)\equiv\frac12\sigma_i^{\gamma}$, where $\sigma_i^{\gamma}$ is the Pauli matrix, is reduced to moderate frustration for the $e_g$ orbital model at $\theta=\pi/3$ [1]. We investigate thermodynamic phase transitions at temperature $T_c$ on an infinite square lattice by variational tensor network renormalization (VTNR) in imaginary time. From the linear susceptibility (order parameter) in the symmetric (symmetry-broken) phase the onset of nematic order in the quantum compass model is estimated at $T_c/J=0.0606(4)$ [2], in good agreement with Quantum Monte Carlo (QMC). For the 2D $e_g$ orbital model one finds: ($i$) a very accurate VTNR estimate of $T_c/J=0.3566\pm 0.0001$ while QMC fails due to the sign problem, and ($ii$) that the critical exponents are within the Ising universality class. Remarkably large difference in frustration and entanglement results in so distinct $T_c$. $ $ [1] L. Cincio, J. Dziarmaga, and A. M. Oleś, Phys. Rev. B **82**, 104416 (2010). [2] P. Czarnik, J. Dziarmaga, and A. M. Oleś, Phys. Rev. B **93**, 184410 (2016).

Speaker: Andrzej M. Oles (Jagiellonian University)

46 Path integral formalism of quantum thermodynamics

Path integral formalism of quantum mechanics and quantum field theory has greatly influenced the theoretical developments of physics. For example, a path integral description of open quantum systems has been used to study the dissipative dynamics of the quantum systems, known as the Caldeira-Leggett model of the quantum Brownian motion. Studies of thermodynamics in the dissipative quantum systems have attracted renewed interest quite recently, owing to the experimental verification of the nonequilibrium equalities and the experimental implementation of quantum information heat engines. In this presentation, we develop a formalism for quantum thermodynamics based on path integral methods. This may give new insights and understandings about the work and heat in quantum systems. In doing so, we use the Caldeira-Leggett model and study the work and heat statistics. This allows us to study the non-Markov, non-rotating wave, strong coupling regime without making any approximations. Using the path integral method, we have derived the quantum work and heat functionals depending on the path integral trajectories of the system. Taking the semi-classical limit, we proved analytically the convergence of the work and heat functionals (and thus their statistics) to their classical counterparts.

Speaker: Ken Funo (Peking University)

47 Quantum measurements of work fluctuations

Work is one of the central notions in (statistical) mechanics and thermodynamics. In fact, it is *the* quantity that connects thermodynamics and mechanics. Unlike in the macroscopic regime, at the microscale, fluctuations of work become relevant and sometimes even dominant, which makes their characterization a question of fundamental importance. In classical mechanics, the solution is straightforward: to each phase-space trajectory, one assigns the value of the work performed along it. In the quantum regime, however, there is no notion of trajectory, and defining fluctuations of work becomes problematic, especially for coherent processes. In this work, we approach the problem in the most general form, and, therefore, consider closed systems and ask whether there exists at all a definition satisfying two minimal conditions: (1) Average work should be given by the difference of initial and final average energies of the system and (2) the classical limit should be respected. Among many possible ways to define the classical limit, we choose arguably the weakest one -- the Jarzynski equality must hold for all thermal initial states. First, we prove that the only work measurement scheme satisfying (2) is the widely-used two-projective-energy-measurements (TPEM) scheme, where the energy is measured both at the beginning and at the end of the process. Second, we show that there exists no state-independent measurement protocol that can simultaneously satisfy (1) for all states and coincide with the TPEM scheme for energy-diagonal initial states. Having thus ruled out the possibility of existence of universal, state-independent generalized quantum measurements for work estimation, we go on asking whether there exist state-dependent schemes capable of satisfying both (1) and (2). It turns out that such measurements do exist, and we describe a simple and intuitive scheme based on the notion of *ergotropy* and its fluctuations as given by a time-reversed TPEM scheme.

Speaker: Karen Hovhannisyan (Department of Physics and Astronomy, University of Aarhus, DK-8000 Aarhus C, Denmark)

12:30 Lunch

Session 6: Panel A

Convener: Prof. Krzysztof Burnecki (Wroclaw University of Science and Technology)

48 Deep learning – results, origin and relation to statistical physics

Machine learning (ML), a fundamental concept of AI research, has recently been dominated by advanced statistical techniques (known as deep learning). The origin the methods comes from network optimization and prior knowledge of brain with serious physics inputs. The progress in theoretical architectural models (such as Recurrent Neural Networks (RNN, Convolutional Neural Networks, Long Short-Term Memory networks (LSTM) and Deep Boltzmann Machines) as well as numerical methods make advanced NN to approximate arbitrary functions better than traditional ML methods given sufficiently large amounts of data. A list of cognitive tasks that deep learning systems beat humans grows monthly. This fact changes the way society operates technologically. Among others, instead of coding (i.e. entitling computers with rules) it would be more effective to teach a system providing data. The examples of applications mainly from Natural Language Processing and understanding area will be given. Increasingly larger number of companies are bringing to market innovative, smart products and services using AI. Search, mapping genotype to phenotype, advanced medical diagnosis and testing and drug creation are one of the most promising applications. Further progress will be achieved by using knowledge from reverse engineered brain functions.

Speaker: Czeslaw Jedrzejek (Poznan University of Technology)

49 Memory in stochastic and chaotic processes

Detection and quantification of presence of memory in various stochastic and chaotic processes is discussed. Short introduction of definitions, signatures, and measures is presented, and several examples of the application of the introduced formalism are discussed in detail. These examples show that nonmarkovian are: most of proceses with stationary correlation function $C(t,s)=C(|t-s|)$ (with notable exception of stationary Ornstein-Uhlenbeck process), chemical reaction, fractional Brownian motions, chaotic processes from Feigenbaum cascade, and quantum processes interacting with heat bath. The discussed methods can be applied also to experimental data in the form of sample paths. It is shown in this way that nonmarkovian are, among others, the driven transport through nanochannels, and Brownian motions of nanoparticles inside living cells.

Speaker: Andrzej Fulinski (M. Smoluchowski Institute of Physics, Jagiellonian University, Łojasiewicza 11, Kraków, Poland Polish Academy of Arts & Sciences, Sławkowska 17, 31-016 Kraków, Poland)

50 Generalized Poisson-Kac processes in statistical physics, thermodynamics and transport

Langevin equations driven by vector-valued Wiener noise represent the prototypical model of evolution equations for a physical system driven by a deterministic velocity field in the presence of superimposed stochastic fluctuations. The statistical nature of a Wiener process can be regarded as the natural legacy of a large number ansatz, in which the effects of many unknown and uncorrelated perturbations justifies the Gaussian nature for the increments of the stochastic forcing. Analogously, in dealing with stochastic field equations (stochastic partial differential equations), ${\partial \phi({\bf x},t)}/{\partial t} = {\mathcal N}[\phi({\bf x},t)] + a(\phi({\bf x},t)) \, f_s({\bf x},t) $, the most common assumption for the stochastic spatio-temporal forcing $f_s({\bf x},t)$ is its delta-correlated nature in space and time ("derivative of a Wiener process"). Notwithstanding the analytical advantages, the assumption of stochastic perturbation of Wiener nature entails some intrinsic shortcomings. The most striking one is the unbounded speed of propagation of stochastic perturbations that, at a microscopic level, is one-to-one with the fractal nature (almost nowhere differentiability) of the graph of a generic realization of a Wiener process. The resolution of the infinite propagation velocity problem has been proposed by C. Cattaneo in the form of a hyperbolic diffusion equation, now bearing his name. In 1974 M. Kac provided a simple stochastic model, for which the associated probability density function is a solution of the Cattaneo equation. In point of fact, it is well known that the Cattaneo model in spatial dimension higher than one does not admit any stochastic interpretation and that the solutions of the Cattaneo model do not preserve positivity. In order to overcome this problem and to provide a stochastic background to the extended thermodynamic theories of irreversible phenomena, the original Kac model has been recently extended and generalized in any spatial dimension via the concept of Generalized Poisson-Kac (GPK) processes. In this presentation, after a brief review of GPK theory we discuss some new results and applications in statistical physics. Specifically: (i) Motivated by the title of the present conference "On the Uniformity of Laws of Nature", it is addressed how Poisson-Kac and GPK processes permit to resolve the "singularities" in the solutions of classical parabolic transport equations. This is not only related to the resolution of the paradox of infinite propagation velocity, but involves also the description of boundary-layer dynamics and the group properties of the associated Markov operator. (ii) The latter issue is closely related to the intrinsic "spinorial" statistical description of GPK processes, that naturally emerges from the relativistic description of stochastic kinematics. (iii) It is addressed how the application of GPK fluctuations in stochastic partial differential equation ensures the preservation of positivity of the field variable (if required by physical principles, for instance whenever $\phi({\bf x},t)$ represents a concentration) and avoids the occurrence of diverging correlation function, problem that arises even in the simplest (linear) stochastic partial differential equations in the presence of delta-correlated noise fields. The most striking example is the Edwards-Wilkinson model in spatial dimensions higher than one. (iv) Finally, the application of GPK is addressed in connection with the modeling of systems of interacting particles.

Speaker: Massimiliano Giona (University of Rome La Sapienza DICMA)

51 An anomalous diffusion approach to stochastic modeling for single molecule tracking of receptors and proteins at cell surface

The Nobel Prize in Physiology or Medicine 2009 was awarded for the discovery of how chromosomes are protected by telomeres and the enzyme telomerase. The Nobel Prize in Chemistry 2012 was given for studies of G-protein-coupled receptors and the Nobel Prize in Chemistry 2014 was presented for the development of superresolved fluorescence microscopy. Definitely, the research behind these Nobel Prizes - awarded within a short few years period - have caused a dramatic increase of experimental and theoretical achievements in the study of living cells around the world. $ $ Ultimately the accessibility of quantitative data prompted many statistical physicists and applied mathematicians to turn their attention to the study of single biological cells and the physiological processes running off therein. For example, G protein-coupled receptors mediate the biological effects of many hormones and neurotransmitters and are major pharmacological targets, [1-4]. However, how receptors and G proteins interact and couple at the plasma membrane is not well understood. $ $ A phenomenon observed in recent single-molecule experiments is anomalous diffusion, which largely departs from the classical Brownian diffusion theory since the mean-squared displacement (MSD) is nonlinear. The most popular theoretical models that are commonly employed are: continuous-time random walk (CTRW), fractional Brownian motion (FBM), fractional Langevin equation (FLE) and autoregressive fractionally integrated moving average (ARFIMA). $ $ Using single-molecule imaging data one can visualize motion of individual receptors and G proteins at the surface of living cells [2]. Here, we provide a detailed anomalous diffusion classification based on MSD analysis [5] for some exemplary experimental data from [2]. $ $ [1] K. L. Pierce, R.T. Premont, R.T. & R.J. Lefkowitz, Seven-transmembrane receptors, Nat. Rev. Mol. Cell. Biol. 3, 639-650 (2002). [2] D. Calebiro, et al. Single-molecule analysis of fluorescently labeled G-protein-coupled receptors reveals complexes with distinct dynamics and organization, Proc. Natl. Acad. Sci. U.S.A. 110, 743-748 (2013). [3] R. 0. Dror, et al. Structural basis for nucleotide exchange in heterotrimeric G proteins, Science 348, 1361-1365 (2015). [4] B. T. DeVree, et al. Allosteric coupling from G protein to the agonist-binding pocket in GPCRs, Nature 535, 182-186 (2016). [5] K. Burnecki, E. Kepten, Y. Garini, G. Sikora, & A. Weron, Estimating the anomalous diffusion exponent for single particle tracking data with measurement errors, Sci. Rep. 5, 11306 (2015).

Speaker: Aleksander Weron (Hugo Steinhaus Center, Faculty of Pure and Applied Mathematics, Politechnika Wrocławska)

Session 6: Panel B

Convener: Dr Anna Ochab-Marcinek (Institute of Physical Chemistry, Polish Academy of Sciences)

52 Principles of design of artifical and biological molecular engines

Molecular engines are based on different principles than macroscopic motors. I will present two examples: artifical engine created in our lab namely nano-wind mill driven by evaporation of water and the motion of kinesin motor walking on microtubules. This biological engine, of incredibly efficiency, is driven by thermal noise, while consumption of ATP is mainly used for detachment of its parts from microtubule. The key principle in its design is the proper synchronization of its diffusion driven by thermal noise with the hydrolysis of ATP, detachment of ADP and further attachement of ATP, as we show in our experiment. Our nano-wind mill does work due to spatial organization and synchronization of many motors, which in concerto respond to flux of water. $ $ The presentation was supported by the National Science Centre, Poland within the grant Maestro UMO-2016/22/A/ST4/00017. $ $ [1] K. Sozanski et al Small Crowders Slow Down Kinesin-1 Stepping by Hindering Motor Domain Diffusion, PHYSICAL REVIEW LETTERS, 115, 218102, (2015). [2] P.Niton et al A "nano-windmill" driven by a flux of water vapour: a comparison to the rotating ATPase, NANOSCALE 5, 9732-9738, (2013). [3] K.Sozanski et al Activation Energy for Mobility of Dyes and Proteins in Polymer Solutions: From Diffusion of Single Particles to Macroscale Flow, PHYSICAL REVIEW LETTERS 111, 228301, (2013). [4] T.Kalwarczyk et al Motion of nanoprobes in complex liquids within the framework of the length-scale dependent viscosity model, ADVANCES IN COLLOID AND INTERFACE SCIENCE 223, 55-63, (2015).

Speaker: Robert Holyst (Institute of Physical Chemistry PAS)

53 Complex dynamics of genomic sites in the nucleus of live cells

The DNA in a human cell is ~3 meters long. It is dynamic and yet is well organized. What are the mechanisms that organizes the chromatin and chromosomes in the nucleus? Using dynamic methods in live cells, we identified a mechanism that maintains the genome organization in the nucleus. We claim that lamin A forms chromatin loops by lamin A dimers (or oligomers) thereby restricting the chromatin dynamics significantly. This can explain the maintenance of chromosome territories in the nucleus. We use advanced methods for studying the dynamics of chromatin and proteins in the nucleus. These methods are based on measuring the signal and fluctuations of fluorescent molecules and the use of biophysical models based on Smoluchowski equation and modified diffusion equations. It allowed us to identify that ~50% of a crucial protein named lamin A is bound to the chromatin everywhere in the nucleus interior. Specific sites along the chromatin commonly exhibit anomalous diffusion (alpha in the range of 0.4-0.7). When lamin A is eliminated, the diffusion dramatically changes to normal diffusion, which is difficult to understand. By analyzing the diffusion in specific time-windows, we show that the dynamics of the genomic sites is bimodal; they are normally constrained and exhibit anomalous diffusion, except for short time-windows where they super-diffuse. By using single-molecule methods including tethered particle motion (TPM) and atomic force microscopy (AFM) we show the type of bonds formed by lamin A and demonstrate the actual bonding that lamin A forms on the DNA.

Speaker: Yuval Garini (Bar Ilan University)

54 Navigation and target search on human chromosomes

In living cells, proteins often bind to specific basepair sequences on DNA, such as transcription factor proteins that regulate gene expression, or restriction enzymes that cut the DNA at cleavage sites. These proteins search for targets that are about 10 basepairs long, on a DNA that is a few mega basepairs in bacteria, and billions in humans. This sounds like a needle in a haystack- problem but search times are surprisingly short. For example, in *E. coli* bacteria it takes a few minutes to locate a gene regulatory site, whereas a random search would take up to ten times longer. The common explanation for this, is that proteins combine three dimensional (3D) excursions with one dimensional (1D) diffusion along the DNA, also known as facilitated diffusion. Combining 3D and 1D search in this way implies that search times depend on the DNA's specific 3D organisation. This has been shown analytically using classical polymer models with known looping probabilities and in simulations. But, how this happens in humans and other eucaryotes where DNA organisation is more complex is an open problem. Theoretically, researchers have been hampered by the lack of knowledge of how eukaryotic DNA is organised, but experimental development of so-called Chromosome Conformation Capture techniques, where state-of-the-art is HiC, have partly remedied this problem. In short, HiC experiments give a genome-wide heat map of physical contact frequencies, or looping probabilities, between all DNA fragments pairs in the cell nucleus down to 1 kilo-basepair resolution. In our recent work, we have used HiC data as a proxy for the *in-vivo* DNA looping probabilities to model protein search on human chromosomes. By mapping the search onto a network problem, with DNA segments as nodes and physical contacts as links, we calculate the mean-first passage time to all nodes for all human chromosomes. For example, we find that DNA segments that harbour gene starts have small search times and are thus easy to find.

Speaker: Ludvig Lizana (Umeå University)

55 Griffiths phases on a large human Open Connectome network

Extended numerical simulations of threshold models have been performed on a human brain network with N=836733 connected nodes available from the Open Connectome Project [1]. While in the case of simple spreading models like contact process, SIS or threshold model a sharp discontinuous phase transition, without any critical dynamics arises, variable threshold models exhibit extended power-law scaling regions. This is attributed to fact that Griffiths effects, stemming from the topological or interaction heterogeneity of the network, can become relevant if the input sensitivity of nodes is equalized. Nonuniversal power-law avalanche size and time distributions have been found with exponents agreeing with the values obtained in electrode experiments of the human brain [2]. Power-law activity time dependences occur sub-critically in an extended control parameter space region without the assumption of self-organization. Probably the most important result of this study is that negative weights enable local sustained activity and promote strong rare-region effects without network fragmentation. Thus, connectomes with high graph dimensions can be subject to rare-region effects and can show measurable Griffiths effects. Another important observation is that power-laws may occur in a single network, without sample averaging, due to the modular topological structure. Link directness, as well as the consequence of inhibitory connections is studied. Robustness with respect of random removal of links suggest that connectome generation errors do not modify the Griffths effects qualitatively. $ $ [1] M.T. Gastner and G. Ódor, Sci. Rep. 5 , 14451 (2015). [2] G. Ódor PRE 94, 062411 (2016).

Speaker: Geza Odor (MTA-EK-MFA, Research Center for Energy, Hungarian Academy of Sciences)

15:30 Coffee break

Session 7: Panel A

Convener: Prof. Martin Bier (East Carolina University)

56 Stochastic dynamics in biological ion channels

The passage of ions through biological cell membranes [1] is essential for life at all levels. It occurs via ion channels through proteins embedded in the membrane, and involves Brownian motion under the influence of powerful electrostatic forces. The permeation process is highly selective, e.g. in valence selectivity a calcium channel selects Ca$^{2+}$ over Na$^+$ by up to 1000:1. There is still no general agreement on the physical mechanism(s) underlying selectivity, but it is known to be associated with fixed negative charge $Q_f$ in a narrow part of the channel called the selectivity filter. There are persuasive arguments [2] that valence selectivity arises from ionic Coulomb blockade (ICB), a phenomenon that is closely analogous to electronic Coulomb blockade in semiconductor devices such as quantum dots and which gives rise to distinct conduction bands and stop-bands as $Q_f$ is varied. We report the first systematic tests [3] of the ICB picture based on experimental, analytical and numerical investigations of the influences of the fixed charge and bulk ionic concentrations on conduction and selectivity in the bacterial NaChBac channel and its mutants. Site-directed mutagenesis and voltage clamp recordings were used to investigate its Na$^+$/Ca$^{2+}$ selectivity, divalent blockade and anomalous mole fraction effect (AMFE). We show that an enhanced ICB model can describe well both the main experimental observations (divalent blockade and AMFE) and the results of Brownian dynamics simulations including the conduction bands and concentration-dependent shifts of the Coulomb staircase of channel occupation. We take account of multi-ion effects, the discreteness of the ionic energy levels, their occupation statistics, and the density of states in the channel, and we consider a generalisation of the theory to encompass selectivity between alike charges [4,5]. These results are not only extending the understanding of ion channel selectivity but also promise applications to biomimetic nanopores with charged walls. $ $ [1] J. Zheng and M. C. Trudeau (eds.), *Handbook of Ion Channels*, CRC Press, Boca Raton, 2015. [2] I. Kh. Kaufman, P. V. E. McClintock, and R. S. Eisenberg, "Coulomb blockade model of permeation and selectivity in biological ion channels", *New J. Phys.* **17**, 083021 (2015). [3] I. Kh. Kaufman, O. A. Fedorenko, D. G. Luchinsky, W. A. T. Gibby, S. K. Roberts, P. V. E. McClintock, and R. S. Eisenberg, "Ionic Coulomb blockade and anomalous mole fraction effect in the NaChBac bacterial ion channel and its charge-varied mutants", *EPJ Nonlinear Biomed. Phys.*, in press (2017). [4] D. G. Luchinsky, W. A. T. Gibby, I. Kh. Kaufman, D. A. Timucin, and P. V. E. McClintock, "Statistical theory of selectivity and conductivity in biological channels", *arXiv preprint* arxiv:1604.05758 (2016). [5] W. A. T. Gibby, D. G. Luchinsky, I. Kh. Kaufman, A. Ward, and P. V. E. McClintock, "Kinetic model of selectivity and conductivity of the KcsA filter", *International Conference on Noise and Fluctuations*, IEEE, doi 10.1109/ICNF.2017.7985935 (2017).

Speaker: Peter McClintock (Department of Physics, Lancaster University)

57 Stochastic modeling of diffusion in dynamical systems: three examples

Consider equations of motion that generate dispersion of an ensemble of particles. For a given dynamical system an interesting problem is not only what type of diffusion is generated by its equations of motion but also whether the resulting diffusive dynamics can be reproduced by some known stochastic model. I will discuss three examples of dynamical systems generating different types of diffusive transport: The first model is fully deterministic but non-chaotic by displaying a whole range of normal and anomalous diffusion under variation of a single control parameter [1]. The second model is a dissipative version of the paradigmatic standard map. Weakly perturbing it by noise generates subdiffusion due to particles hopping between multiple attractors [2]. The third model randomly mixes in time chaotic dynamics generating normal diffusive spreading with non-chaotic motion where all particles localize. Varying a control parameter the mixed system exhibits a transition characterised by subdiffusion. In all three cases I will show successes, failures and pitfalls if one tries to reproduce the resulting diffusive dynamics by using simple stochastic models. $ $ Joint work with all authors on the references cited below. [1] L. Salari, L. Rondoni, C. Giberti, R. Klages, Chaos 25, 073113 (2015) [2] C.S. Rodrigues, A.V. Chechkin, A.P.S. de Moura, C. Grebogi and R. Klages, Europhys. Lett. 108, 40002 (2014) [3] Y.Sato, R.Klages, to be published.

Speaker: Rainer Klages (Queen Mary University of London)

58 Understanding cooperativity and dynamic disorder in fluctuating enzymes at the single molecule level

Single molecule techniques allow researchers to study not only the average reaction rates but also the statistics of single molecule transitions in the context of enzymatic reactions. Such measurements show that the slow fluctuation between enzyme conformers can lead to fluctuations in the rate constants of the reaction, a phenomenon known as dynamic disorder [1]. The most accessible characteristics of reactivity fluctuations in individual enzyme molecules relate to the second moment of turnover time statistics and is defined by the randomness parameter. Measurement of this quantity can serve as an indicator for dynamic disorder in the catalytic step of the reaction. Such enzymatic fluctuations can also lead to deviation in Michaelis- Menten behavior of the reaction rates and the emergence of dynamic cooperativity in single enzymes. In this talk I will discuss about a few such biologically relevant enzyme reaction schemes with multiple binding sites and slow fluctuations between the binding sites. I will propose a simple analytical model based on the first passage time distribution between successive catalytic turnover events that can be used to calculate the average reaction rate and obtain closed-form analytical expressions of the randomness parameter in terms of constant parameters [2, 3]. Our results confirm that slow fluctuations between the free enzyme conformers can lead to dynamic cooperativity whereas dynamic disorder at high substrate concentration is determined only by the slow fluctuations between the enzyme – substrate conformers [4]. Our theoretical findings are well supported by comparison with experimental data on the single enzyme beta-galactosidase [5]. $ $ [1] S. C. Kou, B. J. Cherayil, W. Min, B. P. English and X. S. Xie, J. Phys. Chem. B, 109, 19068-19081 (2005). [2] S. Chaudhury, J. Cao and N. A. Sinitsyn, J. Phys. Chem. B, 117, 503-509 (2013). [3] S. Chaudhury, J. Phys. Chem. B, 118, 10405-10412 (2014). [4] D. Singh and S. Chaudhury, J. Chem. Phys. 146, 145103 (2017). [5] B. P. English, W. Min, A. M. van Oijen, K. T. Lee, G. Luo, H. Sun, B. J. Cherayil, S. C. Kou and X. S. Xie, Nat. Chem. Biol., 2, 87-92 (2006).

Speaker: Srabanti Chaudhury (Indian Institute of Science Education and Research)

59 Evolution of information within sEMG signals in the process of treatment

Colorectal cancer remains to be one among 5 most common types of cancer found for both men and women. Typically multimodal treatment including surgery, radiation and chemotherapy is applied. The electrical activity of external anal sphincter can serve as a potential source of knowledge of the actual state of the patient. The signals registered by means of the surface electromyography are typically highly complex thus create a challenge for its description. The loss of such complexity is often related with the pathological state. Entropy often serves as one of the nonlinear methods capable to grasp an internal structure of the signal together with the insight into its complexity over a wide range of scales. In this work we would discuss the usefulness of the most common techniques for the description of the loss of information carried out by the biomedical signals.

Speaker: Lukasz Machura (University of Silesia)

Session 7: Panel B

Convener: Prof. Paweł Góra

60 Nonuniversality of heat engine efficiency at maximum power

We study the efficiency of a quantum dot engine in the condition of the maximum power output. In contrast to the quasi-statically operated Carnot engine whose efficiency reaches the theoretical maximum, recent research on more realistic engines operated in finite time has revealed other classes of efficiency such as the Curzon-Ahlborn efficiency maximizing the power. The linear coefficient of such power-maximizing efficiency as a function of the reservoir temperature ratio has been argued to be universal as $1/2$ under the tight-coupling condition between thermodynamic fluxes. By taking the quantum dot heat engine, however, we show that depending on the constraint posed on the engine, the linear coefficient can be unity, which implies that the efficiency at the maximum power actually approaches the Carnot efficiency in the equilibrium limit. As a result, we dismiss the notion of universal linear coefficient of the efficiency at the maximum power, and discuss the implication of such a result in terms of entropy production and irreversible thermodynamics. We claim that the particular scheme for the linear coefficient of unity is actually more realistic and experimentally realizable, as it corresponds to controlling the gate voltage of the quantum dot, for given temperatures and chemical potentials of the leads connected to the quantum dot.

Speaker: Sang Hoon Lee (Korea Institute for Advanced Study)

61 Carnot efficiency is attainable in an irreversible process

In thermodynamics, there exists a conventional belief that “the Carnot efficiency is reachable only when a process is reversible.” However, there is no theorem proving that the Carnot efficiency is impossible in an irreversible process. Here, we show that the Carnot efficiency is attainable in an irreversible process through investigation of the Feynman-Smoluchowski ratchet (FSR). Thus, this finding gives us a new possibility to develop a novel design of thermodynamic engines with high efficiency regardless of the reversibility. Our result also answers the long-standing question of whether the Carnot efficiency is possible in the FSR.

Speaker: Jaesung Lee (Korea Institute for Advanced Study)

62 Two forms of heat transfer via interaction with heat bath

We consider a classical open system in contact with heat bath via interaction Hamiltonian. We investigate two forms of energy transfer via the change of interaction Hamiltonian, which are interpreted as heats. One is heat dissipation from the system and the other is heat absorption by the heat bath, which are usually expected to be the same. Since the change of interaction Hamiltonian leads to the difference between the two heats, the two are not the same in non-stationary period. In non-equilibrium stationary state, the two are only equal to each other in average and may differ in probability distribution. We investigate the difference of the forms of heat for toy models and molecular dynamic systems. It will be an interesting question which is a relevant choice of heat used for the first and second laws of thermodynamics. Further study on open quantum systems will be interesting.

Speaker: Chulan Kwon (Myongji University)

63 Identification of spatial diffusivity patches by the wavelet processing of single-particle trajectories

Modern developments in single particle tracking not only open new perspectives for the study of molecular motions in complex environments, but also allow for using these motions as a probe for revealing properties of substrates on which the motions occur. This approach is especially important for studying biological membranes since their non-uniform structure (e.g. due to the presence of protein clusters) results in a large variety of anomalous diffusion phenomena [1]. The first step on this way is providing a map of local diffusion coefficients. Using a standard approach based on moving time averaging of the local squared displacements poses a task of judicious choice of the averaging window, which, for achieving satisfactory accuracy, has to be chosen adaptively, depending on the local diffusion coefficient itself. $ $ This complication may be circumvented by generalizing methods of robust linear fitting based on comlexification of the smooth functions with their subsequent Fourier [2] or Complex Wavelet Transforms (CWT) [3]. For this aim the function $\exp[i\Omega R^2(t)]$, where $R^2(t)$ is the step-wise displacement squared and $\Omega$ is an appropriately chosen factor, is used as an input for the CWT. A modification with respect to [3] is the replacement of the Morlet wavelet by a combination of the Tukey window and the multiplicative decomposition of the exponential factor that assures better spatio-temporal localization. $ $ The method proposed was checked in numerical simulations of random walks on patchy structures with different diffusion coefficients within patches, and was shown to be able to reveal patched structure of diffusion coefficient and to distinguish such situations from random walks with a time-dependent diffusion coefficient. In addition, the method was applied to the experimental data of [1] provided by courtesy of C. Manzo. Its application resulted not only in the demonstration of an existence of substrate patches with slowly varying diffusivity but also allowed for a discussion of a difference between such structures and systems with ergodicity breaking. $ $ EBP is partially supported the Ministry of Education and Science of the Russian Federation within the research project \#3.9499.2017/8.9. $ $ [1] C. Manzo et al., Phys. Rev. X **5** 011021 (2015) [2] E.B. Postnikov, I.M. Sokolov, Physica A **434** 257 (2015) [3] F. Thiel, I.M. Sokolov, E.B. Postnikov, Phys. Rev. E **93** 052104 (2016)

Speaker: Eugene Postnikov (Kursk State University)

64 Some analytical methods of solutions to nonlinear diffusion equation

From a reach family of nonlinear diffusion equations the Burgers’ and Porous Medium equations have been chosen to demonstrate the possibility of getting their analytical solutions of some practically important IBVs problems. A comparison between numerical and analytical solutions have also been provided.

Speaker: Zbigniew Grzywna (Silesian University of Technology, Faculty of Chemistry)

Wednesday, 6 September

Session 8: Panel A

Convener: Prof. Peter McClintock (Lancaster University)

65 Looping and direct transit in Brownian particle escape from force-biased and entropic traps

Recent experiments with single biological nanopores, as well as single-molecule fluorescence spectroscopy and pulling studies of protein and nucleic acid folding raised a number of questions that stimulated theoretical and computational studies of the barrier crossing dynamics. We focus on trajectories of Brownian particles that escape from traps either in the presence of an external force or an entropy potential of a cone. To gain new insights into the escape dynamics, we divide the trajectories into two segments: a looping segment, when a particle unsuccessfully tries to escape returning to the trap bottom, and a direct-transit segment, when it finally escapes moving without returning to the bottom. Analytical expressions are derived for the Laplace transforms of the probability densities of the durations of the two segments. These expressions are used to find the mean looping and direct-transit times as functions of the external force or entropy potential. It turns out that the force/potential dependences of the two mean times are qualitatively different. The mean looping time monotonically increases with the force pushing the particle to the trap bottom or with the increasing entropic barrier at the exit. In contrast to this intuitively appealing result, the mean direct-transit time shows rather counterintuitive behavior: it is reduced by force application independently of whether the force pushes the particles to the trap bottom or to the trap exit and it turns out to be insensitive to the entropy potential.

Speaker: Sergey Bezrukov (National Institutes of Health, Bethesda, MD 20892, USA)

66 Diffusive escape through a narrow opening: new insights into a classic problem

In this talk I overview our recent results [1] on the mean first escape time T of a diffusive particle from a spherical (or a circular) domain enclosed by an impenetrable boundary containing a small escape window. Our settings differ from the classical narrow escape problem in two aspects : First, we introduce explicitly into the model long-range potential interactions of a particle with the boundary, which are always present in realistic situations. Second, we take into account effects of an energy/entropy barrier at the escape window, which were discarded in previous analyses. We develop a self-consistent approximation to derive for T a general expression, akin to the celebrated Collins-Kimball relation in chemical kinetics, which shows that the contibution due to a diffusive search for the escape window and the contribution due to the passage through the escape window are additive. Further on, our analysis reveals that in the true narrow escape limit, where the size of the opening tends to zero, the barrier-induced contribution to T represents the dominant controlling factor such that the narrow escape problem is « barrier-limited » rather than « search-limited ». Next, we analyse the contribution due to diffusive search for the escape window and construct an expansion in powers of the size of the escape window in which the coefficients before the leading terms are expressed as integrals and derivatives of (a rather arbitrary) interaction potential. On example of a triangular-well potential we show that the contribution to T due to diffusive search is non-monotonic with respect to the range of the interaction potential, being minimal for the one having an intermediate extent, neither too concentrated on the boundary nor penetrating too deeply into the bulk. Our analytical predictions are confirmed by numerical simulations. $ $ [1] D. S. Grebenkov and G. Oshanin, Phys. Chem. Chem. Phys. 19, 2723 - 2739 (2017)

Speaker: Gleb Oshanin (Laboratoire de Physique Théorique de la Matière Condensée (UMR CNRS 7600) Sorbonne Universités - UPMC, Paris, France)

67 Anomalous quantum diffusion of hydrogen atoms in proteins

Gerald Kneller Centre de Biophysique Moléculaire CNRS/University of Orléans, France Quasielastic neutron scattering (QENS) from biomolecular systems, such as proteins, probes essentially the diffusive single particle dynamics of the hydrogen atoms. As far as the internal dynamics is considered, the motion of the hydrogen atoms exhibits both multiscale and quantum properties. Starting from the definition for the mean square displacement of a quantum particle, it will be shown how both aspects can be combined within a theory of QENS experiments, which is asymptotically exact for long times/low frequencies and for moderate momentum transfers. $ $ [1] G.R. Kneller, J Chem Phys 145, 044103 (2016) [2] G.R. Kneller, J Chem Phys 134, 224106 (2011)

Speaker: Gerald Kneller (University of Orleans / CNRS)

Session 8: Panel B

Convener: Dr Andrzej Krawiecki (Faculty of Physics, Warsaw University of Technology)

68 Autonomous thermal motors

We present a minimal model of autonomous thermal motor, made of two interacting Brownian particles, sitting on two periodic potentials, and kept at different temperatures. We show that such a system does not require ratchet potentials (with , e.g., an asymmetric saw-tooth shape) in order to exhibit direct transport, but presents a spontaneous symmetry breaking. Both the dynamic and thermodynamic properties of the model are discussed. We find that while the model can be solved exactly in the limit of strong coupling between the particles, the optimal operation regime occurs at moderate coupling strength.

Speaker: Alberto Imparato (University of Aarhus, Department of Physics and Astronomy)

69 Out-of-equilibrium physics in spontaneous synchronization

Spontaneous synchronization is a cooperative phenomenon common in nature which makes oscillators of different frequencies, if strongly coupled, operate together with a single common frequency. Such cooperative effects occur in physical and biological systems over length and time scales of several orders of magnitude. Examples: are flashing of fireflies, rhythmic applause in a concert hall, animal flocking behavior, electrical power-grids, etc. The most celebrated model of synchronization is the Kuramoto model, introduced in 1975, which is simple enough to allow quite a detailed analytical treatment, at the same time capturing several features of realistic systems. After discussing the general dynamical and statistical features of synchronization, I will concentrate on its out-of-equilibrium physical aspects when uncorrelated Langevin noise is added to the model.

Speaker: Stefano Ruffo (SISSA)

70 Lyapunov spectral analysis of randomly coupled systems

The collective dynamics of coupled units arranged on a random network exhibits complex dynamics ranging from synchronization to spatio-temporal chaos. It is often important to identify if perturbations spread across the network or are confined locally, in the presence of quenched disorder. The spectrum of Lyapunov exponents, quantifying the sensitivity to perturbations, can be analyzed analogously to the spectrum of eigenvalues of a random matrix. Simple tools of Random Matrix Theory applied to the Lyapunov spectrum reveal universal features and localization properties emergent from classical deterministic dynamics. $ $ SK Patra & A Ghosh, PRE **93** (3), 032208 [2016], SK Patra & A Ghosh, EPL **117** (6), 60002 [2017].

Speaker: Anandamohan Ghosh (Indian Institute of Science Education and Research Kolkata)

71 Novel ordered phases in coupled driven systems: large compact clusters and fast dynamics

We demonstrate particle clustering on macroscopic scales in a coupled nonequilibrium system where two species of particles are advected by a fluctuating landscape and modify the landscape in the process. The phase diagram generated by varying the particle-landscape coupling, valid for all particle density and in both one and two dimensions, shows novel nonequilibrium phases. While particle species are completely phase separated, the landscape develops macroscopically ordered regions coexisting with a disordered region, resulting in coarsening and steady state dynamics on time scales which grow algebraically with size, not seen earlier in systems with pure domains. $ $ (1) Large compact clusters and fast dynamics in coupled nonequilibrium systems, S Chakraborty, S Pal, S Chatterjee, M Barma, Phys Rev E **93**, 050102(R) (2016). (2) Ordered phases in coupled nonequilibrium systems: static properties, S Chakraborty, S Chatterjee, M Barma, Phys Rev E (accepted), arXiv 1704.03309. (3) Ordered phases in coupled nonequilibrium systems: dynamic properties, S Chakraborty, S Chatterjee, M Barma, Phys Rev E (accepted), arXiv 1704.03320.

Speaker: Sakuntala Chatterjee (S.N. Bose National Centre for Basic Sciences, Kolkata, India)

10:30 Coffee break

Session 9: Panel A

Convener: Prof. Ralf Metzler (University of Potsdam)

72 Eliminating inertia of a stochastic microswimmer with constant speed

An often used model for an active entity is the two dimensional stochastic microswimmer. It moves due to a propulsive mechanism with constant speed and changes the direction due to deterministic and random torques. Despite the simplicity, the model it is not an overdamped situation. Intertia is reflected by an initial ballistic behaviour. Only after an crossover time being the relaxation time of the orientational directions the motion becomes normally diffusive characterized by a diffusion coefficient. $ $ In the report I discuss the properties and the distribution of displacements of the stochastic microswimmer with constant speed. Various situations with several random torques like Gaussian white noise, an Ornstein-Uhlenbeck process and alpha-stable noise will be studied. Special attention is devoted to the adiabatic elimination of inertia in the model and the derivation of the overdamped limit. It results for all types of random torques in a Gaussian simplification similar to a Brownian particle driven by white noise. Therein the noise intensity addresses the specific noise sources. $ $ J. Nötel, I.M. Sokolov, L. Schimansky-Geier, „Diffusion bof active particles with stochastic torques modeled as alpha-stable noise“, Journal of Physics A: Mathematical and Theoretical **50** (3), 034003 (2016). S. Milster, J. Nötel, I.M. Sokolov, L. Schimansky-Geier, „Eliminating inertia in a stochastic model of a microswimmer with constant speed“, Eur. Phys. J. Special Topics **226**, 2039-2055 (2017). J. Nötel, I.M. Sokolov, L. Schimansky-Geier, „Gaussian appproximation of the stochastic microswimmer driven by alpha-stale noise, submitted for publication.

Speaker: Lutz Schimansky-Geier (Department of Physics, Humboldt-University at Berlin)

73 Heterogeneous continuous time random walk on graphs

Solute transport and, particularly, diffusion of particles in porous media is a long standing problem [1]. The general random walks framework has been shown to describe quantitatively the anomalous transport patterns frequently observed in fractured and heterogeneous porous media [2]. One of the major conceptual difficulties consists in a very broad range of time and length scales in the dynamics [3] that prohibits using conventional theoretical approaches or numerical simulation methods. $ $ To overcome this problem and bridge various scales, we present a new model, Heterogeneous Continuous Time Random Walk model (HCTRW) and suggest to represent a porous medium by an equivalent “porous graph” and then to model the complex dynamics of a particle in the porous medium by a continuous time random walk (CTRW) on that porous graph. The graph structure accounts for the inter-connectivity of pores, whereas their geometric properties (shapes of pores and of connectivity regions) are, to some extent, captured through the CTRW characteristics, hence connecting the topological and dynamical properties of the system. In our CTRW approach, the space and time characteristics of individual jumps on a graph are coupled that requires developing new theoretical tools. We present several preliminary results on the long-time asymptotic behavior of a particle on a porous graph. To validate the proposed coarse-graining scheme, we compare the asymptotic behavior of the CTRW on a porous graph with the original continuous dynamics in several models of porous media. In particular, we investigate how topology of a graph (which would correspond to i.e. the interconnectivity of pores) can affect the long-time behavior of HCTRW. $ $ [1] R. Friedrich, J. Peinke, M. Sahimi, M. R. R. Tabar, “Approaching complexity by stochastic methods: From biological systems to turbulence”, Phys. Rep. **506**, 87-162 (2011) [2] H. Scher and M. Lax, “Stochastic Transport in a disordered solid. I. Theory”, Phys. Rev. B **7**, 4491 (1973) [3] P. Levitz, V. Tariel, M. Stampanoni, and E. Gallucci, “Topology of evolving pore networks”, Eur. Phys. J. Appl. Phys. **60**, 24202 (2012)

Speaker: Liubov Tupikina (Ecole Polytechnique)

74 Dynamics of self-propelled colloidal particles in viscoelastic fluids

The motion of many natural microswimmers, e.g. bacteria and spermatozoa, commonly takes place in viscoelastic fluids and under confinement close to solid walls. The understanding of their swimming mechanisms has triggered a lot of experimental and theoretical work in recent years as well as the development of self-propelled colloidal particles. Although the motion of such synthetic microswimmers in Newtonian fluids has been extensively studied, and they are nowadays a paradigm in non-equilibrium soft matter [1], so far only few investigations have focused on the swimming of microorganisms in viscoelastic fluids [2]. In our work, we experimentally investigate the dynamics of spherical colloidal microswimmers in viscoelastic fluids, which are self-propelled by local demixing of a critical binary polymer mixture induced by laser illumination. Unlike the motion in Newtonian liquids, we observe a pronounced enhancement of rotational diffusion with increasing particle velocity [3], thereby revealing an unexpected breakdown of the Stokes-Einstein relation for the particle orientation. We demonstrate that this non-equilibrium effect originates from the coupling between the directed particle motion, and the slow microstructural relaxation of the surrounding fluid [4]. Furthermore, we show that such a coupling gives rise to a wealth of new non-equilibrium phenomena with no counterpart in Newtonian liquids, e.g. for the particle translational and rotational dynamics close to solid walls, as well as for collective motion in crowded environments. $ $ References $ $ [1] C. Bechinger, R. Di Leonardo, H. Löwen, C. Reichhardt, G. Volpe, and G. Volpe, Rev. Mod. Phys. 88, 045006 (2016). [2] A. Patteson, A. Gopinath, and P. E. Arratia, Curr. Opin. Colloid Interface Sci., 21, 86 (2016). [3] J. R. Gomez-Solano, A. Blokhuis, and C. Bechinger, Phys. Rev. Lett. 116, 138301 (2016). [4] J. R. Gomez-Solano, and C. Bechinger, New J. Physics 17, 103032 (2015).

Speaker: Juan Ruben Gomez Solano (Universitaet Stuttgart)

75 The quantum first detection problem: from the energy spectrum to the detection probabilities

We consider the question of when a quantum system initially prepared in state A first ``arrives'' in state B, i.e. the first arrival problem in quantum physics. To determine the arrival, the observer attempts to detect the system stroboscopically with fixed period via a projective measurement. The time of the first successful detection attempt is the first detection time. The corresponding probability of the event is the first detection probability. For systems with a continuous energy spectrum, this quantity can be expressed in terms of the spectral measure of the evolution operator (which is related to the density of energy states). This allows us to present an exact formula for the total probability of detection and to derive the long-time asymptotic behavior of the first detection probabilities. It is shown that the latter decays like a power law with superimposed oscillations. The exponent of the power law is determined by the spectral (or fracton) dimension of the spectral measures. The total probability of detection is always less than unity.

Speaker: Felix Thiel (Bar-Ilan University)

76 Switching of wake-mediated interaction caused by blockade effect and collective wake formation

The effect of concentration-dependent switching of the wake-mediated interaction between obstacles in a gas flow of interacting Brownian particles is presented. When increasing bath fraction exceeds half-filling, the interaction between obstacles switches from effective attraction to repulsion or vice-versa, depending on the mutual alignment of obstacles with respect to the gas flow. It is shown that for an ensemble of small and widely separated obstacles the dissipative interaction takes the form of induced dipole-dipole interaction governed by an anisotropic screened Coulomb-like potential. This allows one to give a qualitative picture of the interaction between obstacles and explain switching effect as a result of changes of anisotropy direction. The non-linear blockade effect is shown to be essential near closely located obstacles, that manifests itself in the additional screening of gas flow and generation of a pronounced step-like profile of gas density distribution. It is established that behavior of the magnitude of dissipative effective interaction is, generally, non-monotonic in relation to both the bath fraction and the external driving field. It has characteristic peaks corresponding to the situation when the common density "coat" formed around the obstacles is most pronounced. The possibility of the dissipative pairing effect and the effects of enhanced shock-wave formation of wake profiles under the collective scattering of gas flow on impurities are discussed. All the results are obtained within the classical lattice-gas model.

Speaker: Oleksandr Kliushnychenko (Institute of Physics, NASU, Kiev, Ukraine)

Session 9: Panel B

Convener: Dr Jeremi Ochab (M. Smoluchowski Institute of Physics, Jagiellonian University, Kraków)

77 Diffusion and dynamic scaling in concentrated charge-stabilized colloidal suspensions

We present a joint theory, simulation and experimental study of collective and self-diffusion in concentrated suspensions of charged colloidal particles. The study is based on the generalized Smoluchowski diffusion equation accounting both for direct and solvent-mediated hydrodynamic interactions, and it spans the range from the colloidal short-time to the long-time regime. Owing to the large size asymmetry between the colloidal macroions and the neutralising microns, the degrees of freedom of the latter can be integrated out, resulting in an effective (microion-dressed) colloid pair potential characterised by a renormalised colloid charge and Debye screening parameter. Various state-of-the-art methods of calculating such an effective colloid interaction potential are compared for suspensions in osmotic equilibrium with a salt reservoir. The effective colloid potential is used as input in our accelerated Stokesian Dynamics (ASD), Brownian Dynamics (BD) and self-consistent mode-couling theory (MCT) calculations of intermediate and self-intermediate scattering functions and particle mean-squared displacements. On basis of these numerical results that are compared in addition with dynamic light scattering data on silica particles suspensions, the influence of hydrodynamic interactions on self- and collective diffusion, and the accuracy of the MCT method are quantified. A proposed time-wavenumber scaling relation between short- and long time diffusion properties is shown to be violated in general.

Speaker: Gerhard Naegele (Forschungszentrum Jülich, ICS-3)

78 Exact solution for a $1+1$ etching model.

We present a method to derive analytically the growths exponents of a eroded surface whose dynamics is ruled by cellular automata. Starting from the automata, we write down the time evolution for the height's average and height's variance (roughness). We apply the method to the etching model[1,2] of $1+1$ dimensions, than we obtain the dynamical exponents, which perfectly match the numerical results obtained from simulations. Those exponents are exact and they are the same as those exhibited by the KPZ model[3] for this dimension. Therefore, it shows that the etching model and KPZ belong to the same universality class[4]. Moreover, we proof that in the continuous limit the majors terms leads to KPZ [5]. $ $ [1] B. A. Mello, A. S. Chaves, and F. A. Oliveira, Phys. Rev. E 63, 041113 (2001). [2] E. A. Rodrigues, B. A. Mello, and F. A. Oliveira, J. Phys. A 48, 035001 (2015). [3] M. Kardar, G. Parisi, and Y. C. Zhang, Phys. Rev. Lett. 56, 9, 889 (1986). [4] W. S. Alves, E. A. Rodrigues, H. A. Fernandes, B. A. Mello, F. A. Oliveira and I. V. L. Costa, Phys. Rev. E 94, 042119 (2016). [5] W. P. Gomes and F. A. Oliveira, to be published.

Speaker: Fernando Oliveira (Universidade de Brasília)

79 Subdiffusion in a system consisting of two different media

We consider subdiffusion in a system which consists of two homogeneous media joined together; subdiffusion parameters can be different in both media [1,2]. We also consider subdiffusion with absorption in a composite system. The application of the theoretical model to describe a real diffusion processes in the considered system is also presented. Confronting the theoretical formulas with the experimental data we estimate subdiffusive parameters of colistin in aqueous agarose solution and we show the subdiffusive character of colistin transport in the gel. $ $ [1] T. Kosztołowicz, Int. J. Heat Mass Transf. 111, 1322 (2017). [2] T. Kosztołowicz, J. Chem. Phys. 146, 084114 (2017).

Speaker: Tadeusz Kosztolowicz (Institute of Physics, Jan Kochanowski University in Kielce)

80 Random dynamics in a trap: killing vs survival

We consider the random dynamics in a bounded domain, while concentrating on somewhat unexplored links between the absorbing and inaccessible boundarz data impact upon random motion. Both Brownian and Levy-stable dynamics will be discussed , with a focus on tyhe long term surival, and the permanent trapping scenarios.

Speaker: Piotr Garbaczewski (University of Opole)

12:35 Lunch

EPS

Convener: Prof. Christian Beck (Queen Mary, University of London)

81 What is Complexity?

We have now institutes for complex systems, conferences on complex systems, and journals of complex systems. So most of us have a good feeling what is a complex system. But what is complexity itself, and is there any way to measure it? The answer to this is surprisingly non-trivial. Indeed, there is no universally agreed concept, according to which a bacterium is more complex than a human. But how can we do complex systems science, if we cannot measure complexity? How would we do thermodynamics, if we could not measure temperature? In this talk I will not give answers, but I will discuss several approaches that give partial answers at least.

Speaker: Grassberger Peter (Forschungszentrum Juelich)

82 A bird's eye view of Nonlinear Physics

The special challenge of Nonlinear Physics is that every new problem calls for a specialized idea and a new method to solve it. There exist almost no "general" methods in the arsenal. I will review my own forays into the nonlinear domain stressing this challenge and highlighting the few lucky strikes that I had been involved in during more than 35 years of research.

Speaker: Itamar Procaccia (The Weizmann Institute of Science)

83 Measuring effective temperatures in a Generalized Gibbs ensemble

In Gibbs equilibrium, fluctuation-dissipation relations can be generically used to probe the thermal properties of the system and measure its temperature. When the system under study is integrable, though, the dynamics fails to approach such a Gibbs state, reaching instead a generalized ensemble with a macroscopic number of temperature-like parameters which enforce the value of the underlying conserved quantities. In this setting we show that generalized fluctuation-dissipation relations for appropriately chosen -- yet very physical -- observables, can be used to infer such temperatures allowing us to reconstruct the non-thermal state. These results can be applied to a large variety of models including the one dimensional Bose gas where the relevant correlation function is provided by the structure factor, a quantity that can be experimentally accessed.

Speaker: Laura Foini (École Normale Supérieure, Paris)

84 Generic properties of stochastic entropy production

The laws of thermodynamics can be extended to mesoscopic systems for which energy changes are on the order of the thermal energy are relevant. Therefore, thermodynamic observables associated with mesoscopic degrees of freedom are stochastic. A key example of such thermodynamic observable is the stochastic entropy production in nonequilibrium processes. Little is known beyond fluctuation theorems about universal or model-independent statistics of entropy-production fluctuations. $ $ Using Martingale theory we have discovered novel universal statistics of stochastic entropy production in nonequilibrium steady states such as: (i) The distribution of the negative record (which we call infimum) of entropy production (ii) the passage probabilities of entropy production; (iii) the stopping-time fluctuations of entropy production. $ $ For nonequilibrium Langevin processes, we derive an Ito stochastic differential equation for entropy production. Introducing a random-time transformation, entropy production obeys a one-dimensional drift-diffusion equation, independent of the underlying physical model. This transformation allows to identify novel generic properties of entropy production. It also leads to an exact uncertainty equality relating the Fano factor of entropy production and the Fano factor of the random time. $ $ Our results have interesting implications for stochastic processes that can be discussed in colloidal systems and active molecular processes. For example, we make predictions for the distribution of the maximum backtrack depth of RNA polymerases during RNA transcription in eukaryotes. $ $ [1] É. Roldán, I. Neri, M. Dörpinghaus, H. Meyr and F. Jülicher, Phys. Rev. Lett. 115 (25), 250602 (2015). [2] I. Neri, É. Roldán, and F. Jülicher, Phys. Rev. X 7, 011019 (2017). [3] S. Pigolotti, I. Neri, É. Roldán, and F. Jülicher, arXiv:1704.04061 (2017).

Speaker: Edgar Roldan (Max Planck Institute for the Physics of Complex Systems)

16:10 Coffee break

EPL

Convener: Prof. John Enderby (Sir)

85 The (random) matrix reloaded. Old tricks for new dogs - and return

Matrices with random entries - much like cats - enjoy several lives. Studied in one context, they usually prove more useful in another, giving rise to more and more baffling challenges and unexpected twists as time goes by. But, the field of random matrices is also plagued by false myths, inaccurate historical accounts, and true gems that - while jealously kept from our colleagues - would certainly deserve a better fate. I will give a cheerful account of the ‘old tricks’ of the trade in the occasion of the 89th birthday of Random Matrix Theory, and how well they assist us with a few - nasty - ‘new dogs’. Also, how technical advancements in the field have made it possible - at long last - to make significant progresses in our understanding of old problems. In the course of my talk, I will likely get many cats out of the bag - as progress in science often relies on not letting sleeping dogs lie!

Speaker: Pierpaolo Vivo (King's College London)

86 Random matrices meet trapped fermions

I will review some recent results exploring the connection between non-interacting fermions in a d-dimensional trapping potential and random matrix theory. The presence of the trap introduces an edge where the average density of fermions vanishes. Far from the edge, near the centre of the trap (the so called "bulk regime"), physical properties of the fermions have traditionally been understood using the Local Density Approximation. However, this approximation drastically fails near the edge where the density vanishes. In this talk, I will show that, even near the edge, novel universal properties emerge, independently of the details of the confining potential. These universal correlations can be described by random matrix theory (in one dimension and at zero temperature) and by more general determinantal processes in higher dimensions and finite temperature. $ $ D. S. Dean, P. Le Doussal, S. N. Majumdar, G. Schehr, Phys. Rev. Lett. **114**, 110402 (2015), EPL **112**, 60001 (2015), Phys. Rev. A **94**, 063622 (2016).

Speaker: Gregory Schehr (Universite Paris-Sud, CNRS)

17:45 Reception (sponsored by EPL)

Thursday, 7 September

14:00 Collegium Maius Tours

contact Ewa Witkowska

15:30 Coffee Break

Poster Session

19:00 Banquet

Friday, 8 September

Session 12: Panel A

Convener: Prof. Fernando Oliveira (Universidade de Brasília)

87 Individual and network heterogeneity in agent-based models

Most applications of Statistical Mechanics methods to agent-based models make assumptions that aim at a simplification of the mathematical treatment and which are reasonable, or well established, in other applications of the field. Amongst others, we can cite the assumption of the thermodynamic limit and the assumption that there is a high degree of homogeneity amongst the agents. This is certainly not true in most cases: the number of agents is never close to the Avogadro number and the dispersion in the individual features of agents is an unavoidable nature of the system. In this talk I will discuss some difficulties associated to the existence of such a heterogeneity and the mathematical tools that can be used to achieve analytical results. As an example, I will consider in detail both network and parametric heterogeneity in Kirman’s model for herding behavior in financial markets. Stylized facts of financial markets (fat tails, volatility clustering) has been proposed as an emergent phenomenon of interactions among traders. One of the simplest agent-based models capable of reproducing these statistical properties is the one proposed by Kirman. The fundamental aspect of the model is that agents change opinion based on the proportion of neighbor agents holding it. The effect of network structure on the results of the model is also addressed with recent analytical tools known as heterogeneous mean field approximations. This approach suggests that the dynamics in an heterogeneous degree network is equivalent to the usual all-to-all approximation with an effective system size $N_{\textrm{eff}}=N \mu_{1}^2/\mu_{2}$, where $\mu_{k}$ is the *k*-th moment of the degree distribution. This implies that highly heterogeneous degree networks are characterized by a low effective population number. Intuitively, only highly connected agents play an important role in the dynamics and the number of those agents is measured by this effective population number. Taking into account that most real networks are highly heterogeneous with power-law degree distributions, one concludes that the effect finite-size fluctuations is non-trivial and must be studied in detail for each specific type of network.

Speaker: Raul Toral (IFISC)

88 Coordination games on networks

One of the key contributions of Marian Smoluchowski was to show that even small, apparently random, contributions from individuals can combine to produce significant shifts in the collective behaviour. This paradigm is not limited to physics but has become increasingly influential in biological and social sciences. Models have been developed to describe such diverse systems like the market failure or spread and control of infectious diseases. We present a model that combines game theoretical framework for decision-making process involved in controlling plant infection or pest spread with a network model. We study a repeated cooperation game describing actions of plant nursery managers. We show that although the cooperation strategy is not stable (due to the existence of a risk-dominant strategy), the decay rate non-trivially depends on the initial density of cooperators, on the weight they assign to past events, and whether the decision involves an element of a chance. By considering an agent quantal response learning process, we also study how ‘irrationality’ of decisions influence potential for collaborative actions. Finally, we show that the network structure also impacts on the emergence of cooperation.

Speaker: Adam Kleczkowski (University of Stirling, Scotland)

89 Mean-potential law in evolutionary games

We formulate two simple and intuitive criteria for evolutionary stability of pure Nash equilibria in stochastic dynamics of finite populations. Our approach is based on the mapping of continuous stochastic dynamics into discrete ones and the appropriate choice of potential functions. We present the correspondence between one-dimensional stochastic differential equations describing diffussion with a state-dependent drift and discrete-space random walks, which is exact even in finite-state spaces. This enables us to compute fixation probabilities in various stochastic dynamical systems with two absorbing states.

Speaker: Jacek Miekisz (Institute of Mathematics, Polish Academy of Sciences and University of Warsaw)

90 Spin-glass-like transition in the majority vote model with contrarians

Majority vote model on random graphs and scale-free networks is investigated, in which a fraction p of agents (called contrarians or anticonformists) follows an antiferromagnetic update rule, i.e., they assume, with probability governed by a parameter q (0 < q < 1/2), the opinion opposite to that of the majority of their neighbors, while the remaining 1-p fraction of agents follows the usual ferromagnetic update rule assuming, with probability governed by the same parameter q, the opinion in accordance with that of the majority of their neighbors. For p=1 it is shown by Monte Carlo simulations and using the Binder cumulants method that for decreasing q the model undergoes second-order phase transition from a disordered (paramagnetic) state to a spin-glass-like state, characterized by a non-zero value of the spin-glass order parameter measuring the overlap of agents' opinions in two replicas of the system, and simultaneously by the magnetization close to zero. Besides, in this state the correlation of the agents' opinions exhibits exponentially decaying oscillations, as expected in the spin-glass phase. In the case of the model on scale-free networks the critical value of the parameter q weakly depends on the details of the degree distribution. As p is decreased, the critical value of q falls quickly to zero and only the disordered phase is observed. On the other hand, for p close to zero for decreasing q the usual ferromagnetic transition is observed.

Speaker: Andrzej Krawiecki (Faculty of Physics, Warsaw University of Technology)

Session 12: Panel B

Convener: Prof. Aleksei Chechkin (Institute for Physics and Astronomy, University of Potsdam)

91 A Boltzmann-distribution-equivalent for Levy noise and how it leads to thermodynamically consistent epicatalysis

Nonequilibrium systems commonly exhibit Levy noise. This means that the distribution for the size of the Brownian fluctuations has a "fat" power tail. Large Brownian kicks are then more common as compared to the ordinary Gaussian distribution that is associated with equilibria. $ $ We consider a two-state system, i.e. two wells and in between a barrier that is sufficiently high for a barrier crossing to be a rare event. When the noise is Levy, we do *not* get a Boltzmann distribution between the two wells. Instead we get a situation where the distribution between the two wells also depends on the height of the barrier that is in between. $ $ A catalyst, by lowering the barrier between two states, can speed up the establishment of an equilibrium. It will, however, not change the equilibrium distribution. In an environment with Levy noise, on the other hand, we have the possibility of epicatalysis, i.e. a catalyst effectively altering the steady state distribution between two states by changing the barrier height. We discuss how this idea may possibly apply to nuclear reactions and to biochemical reality in a living cell.

Speaker: Martin Bier (East Carolina University)

92 Stochastic processes for fractional kinetics with application to anomalous diffusion in living cells

Fractional kinetics is derived from Gaussian processes when the medium where the diffusion takes place is characterized by a population of length-scales [1]. This approach is analogous to the generalized grey Brownian motion [2], and it can be used for modelling anomalous diffusion in complex media. In particular, the resulting stochastic process can show sub-diffusion, ergodicity breaking, p variation, and aging with a behaviour in qualitative agreement with single-particle tracking experiments in living cells. Moreover, for a proper distribution of the length-scales, a single parameter controls the ergodic-to-nonergodic transition and, remarkably, also drives the transition of the diffusion equation of the process from nonfractional to fractional, thus demonstrating that fractional kinetics emerges from ergodicity breaking [3]. $ $ [1] Pagnini G. and Paradisi P., A stochastic solution with Gaussian stationary increments of the symmetric space-time fractional diffusion equation. Fract. Calc. Appl. Anal. 19, 408–440 (2016) [2] Mura A. and Pagnini G., Characterizations and simulations of a class of stochastic processes to model anomalous diffusion. J. Phys. A: Math. Theor. 41, 285003 (2008) [3] Molina–García D., Pham T. Minh, Paradisi P., Manzo C. and Pagnini G., Fractional kinetics emerging from ergodicity breaking in random media. Phys. Rev. E. 94, 052147 (2016)

Speaker: Gianni Pagnini (BCAM - Basque Center for Applied Mathematics, Bilbao, Basque Country - Spain)

93 Microscopic derivation of coloured Lévy flights in active swimmers' suspensions

The motion of a tracer particle in a complex medium typically exhibits anomalous diffusive patterns, characterised, e.g, by a non-liner mean-squared displacement and/or non-Gaussian statistics. Modelling such fluctuating dynamics is in general a challenging task, that provides, despite all, a fundamental tool to probe the rheological properties of the environment. A prominent example is the dynamics of a tracer in a suspension of swimming microorganisms, like bacteria, which is driven by the hydrodynamic fields generated by the active swimmers. For dilute systems, several experiments confirmed the existence of non-Gaussian fat tails in the displacement distribution of the probe particle, that has been recently shown to fit well a truncated Lévy distribution. This result was obtained by applying an argument first proposed by Holtsmark in the context of gravitation: the force acting on the tracer is the superposition of the hydrodynamic fields of spatially random distributed swimmers. This theory, however, does not clarify the stochastic dynamics of the tracer, nor it predicts the non monotonic behaviour of the non-Gaussian parameter of the displacement distribution. Here we derive the Langevin description of the stochastic motion of the tracer from microscopic dynamics using tools from kinetic theory. The random driving force in the equation of motion is a coloured Lévy Poisson process, that induces power-law distributed position displacements. This theory predicts a novel transition of their characteristic exponents at different timescales. For short ones, the Holtzmark-type scaling exponent is recovered; for intermediate ones, it is larger. Consistently with previous works, for even longer ones the truncation appears and the distribution converge to a Gaussian. Our approach allows to employ well established functional methods to characterize the displacement statistics and correlations of the tracer. In particular, it qualitatively reproduces the non monotonic behaviour of the non-Gaussian parameter measured in recent experiments.

Speaker: Andrea Cairoli (Imperial College London)

94 Second order optimization may lead to Lévy walks

Most living organisms perform two different types of search: a directed search (taxis) and a random search. The former is observed when the environment provides cues to guide the motion towards targets, whereas the latter may not involve any memory and information processing and can be modeled by ran- dom walks. There is a large body of experimental results showing that the random walk adopted by many organisms is described well by Lévy walks, which raises questions about the reasons and underlying mech- anisms of such a behavior. Here we show that Lévy walks may emerge from a directed gradient based search, which bridges the gap between the two modes of a search. For a wide range of scenarios our model reproduces the tail index α = 1, in line with previous experimental observations in foraging organisms and predictions based on optimality considerations for sparse targets. Moreover, the model predicts specific relations between features of the search and the curvature of the optimized function, which can be tested experimentally.

Speaker: Lukasz Kusmierz (RIKEN Brain Science Institute)

95 Operational method for fractional Fokker-Planck equation

I will present the results for fractional equations of Fokker-Planck type using evolution operator method. I will employ exact forms of one-sided Levy stable distributions to generate a set of self-reproducing solutions. Explicit cases are reported and studied for various fractional order of derivatives, different initial conditions, and for different versions of Fokker-Planck operators.

Speaker: Katarzyna Gorska (Institute of Nuclear Physics, Polish Academy of Sciences)

Session 12: Panel C

Convener: Prof. Lech Longa (Jagiellonian University)

96 Bottlebrush polymers: from dilute solutions to super-soft rubbers

Polymer bottlebrushes provide intriguing features being relevant both in nature and in synthetic systems. While their presence in the articular cartilage optimizes synovial joint lubrication, bottlebrushes offer pathways for fascinating applications, such as within super-soft elastomers or for drug delivery. However, the current theoretical understanding lacks completeness, primarily due to the complicated interplay of many length scales. During the talk new analytical model of bottlebrush polymers will be presented. The model applies to solutions ranging from dilute concentrations to dense melts. The validity of our model is supported by data from extensive molecular dynamics simulation. We demonstrate that the hierarchical structure of bottlebrushes dictates a sequence of conformational changes as the solution concentration increases. The effect is mediated by screening of excluded volume interactions at subsequent structural parts of the bottlebrushes. Our findings provide important insights that should enable improved customization of novel materials based on the architectural design of polymer bottlebrushes.

Speaker: Jaroslaw Paturej (University of Szczecin)

97 Translational and rotational Brownian motion of particles of complex shapes

The characteristic time scales of the translational and rotational Brownian diffusion for nanoparticles are typically much smaller than time resolution of the experiments. In this case, nanoparticles can be treated as point-like, and described by the standard Brownian theory. However, for microparticles, the characteristic Brownian time scales are of the order of seconds, and therefore non-negligible in comparison to the typical time scales of the measured Brownian motion. For microparticles of complex shapes, a more general theoretical approach is needed. The exact analytical expressions for the time-dependent cross-correlations of the translational and rotational Brownian displacements of a particle with arbitrary shape have been recently derived [1,2], and it has been demonstrated how to benefit from these results while analyzing experimental data [3]. $ $ [1] Cichocki B., Ekiel-Jeżewska M. L., Wajnryb E., J. Chem. Phys. 142, 214902, 2015. [2] Cichocki B., Ekiel-Jeżewska M. L., Wajnryb E., J. Chem. Phys. 144, 076101, 2016. [3] Cichocki B., Ekiel-Jeżewska M. L., Wajnryb E., Arch. Mech. 69, 1. 2017.

Speaker: Maria L. Ekiel-Jezewska (Institute of Fundamental Technological Research, Polish Academy of Sciences)

98 Forces from temperature quenches in thermal and active matter

Non-equilibrium systems are known to exhibit long-ranged correlations in the presence of dynamical conservation laws. This phenomenon gives rise to various types of fluctuation-induced forces between objects immersed in non-equilibrium media. However, driving systems out of equilibrium, for instance by changing their temperature, may also result in changes of the mean density. $ $ In this talk I will discuss our recent work on non-equilibrium fluctuation-induced (Casimir) forces [1,2] and density-induced forces [2] arising from temperature quenches in thermal and active matter. Focusing on temperature quenches, we predict theoretically and demonstrate with simulations the existence of both these types of forces between objects immersed in a conserved density. (In active matter, a quench could be achieved by a rapid change in activity.) We discuss the distinguishing features of fluctuation-induced and density-induced forces as regards universality, time-scales and scaling. By considering microscopic theories and coarse-graining procedures, we propose methods to extract the fluctuation-induced contribution of forces in simulations. Simulation results [2] display the scaling in space and time predicted in [1]. $ $ [1] C.M. Rohwer, M. Kardar, M. Krüger, Phys. Rev. Lett. 015702 **118** (2017) [2] C.M. Rohwer, A. Solon, M. Kardar, M. Krüger, *in preparation* (2017)

Speaker: Christian Rohwer (Max Planck Institute for Intelligent Systems)

99 Dynamics of diluted confined systems

Recent studies have shown that the presence of boundaries can strongly affect the dynamics of physical systems. For example, negative mobility and fluid recirculation occurs when an electrolyte is driven in a varying-section channels[1], rectification occurs active particles such as molecular motors[2] or active swimmers[3] moving in inhomogeneous environments and off--diagonal terms in the mobility tensor appears for binary mixtures of hard sphere confined between corrugated plates[4]. Clearly the interplay between the confined systems and the confining walls is maximized when the typical length scales of the confined system match with the size of the confining walls. In this contribution I will discuss the general mechanisms at the basis of the interplay between the confined system and the confinement. In particular, by means of a few example I will show how analytical insight into the possible regimes can be attained. $ $ Firstly, I will discuss how the electrostatic interaction between a tracer particle and the channel walls affect particle dynamics. In such a scenario, novel dynamical regimes such as negative mobility[1] and asymmetric passage times[5] can arise due to the interplay between the electrostatic interactions and the local entropic drive induced by the varying--section channel. $ $ Secondly I will show how the insight gained by such studies can be transferred to the problem of polymer translocation across varying-section channels. In particular, I will show that, under suitable approximation, it is possible to reduce the problem of polymer translocation across varying-section channels to that of a single point--like particle under an effective potential that can be derived from the equilibrium local free energy of the polymer. Interestingly, the model predicts a non-monotonous dependence on the translocation time of the polymer across the pore appears. By comparing with Brownian dynamics simulations I will discuss the quantitative reliability of the point-like approximation as well as its regime of validity[6]. $ $ [1] P. Malgaretti, I. Pagonabarraga and M.J. Rubi: PRL **113** 128301 (2014) [2] P. Malgaretti, I. Pagonabarraga and M.J. Rubi: Phys. Rev. E **85** 010105 (2012) [3] P. Malgaretti and Holger Stark, J. Chem. Phys. **146**, 174901 (2017) [4] U. Marini Bettolo Marconi, P. Malgaretti and I. Pagonabarraga: J. Chem. Phys. **143** 184501 (2015) [5] P. Malgaretti, I. Pagonabarraga and M.J. Rubi: J. Chem. Phys. **144** 034901 (2016) [6] V. Bianco and P. Malgaretti J. Chem. Phys. **145** 114904 (2016)

Speaker: Paolo Malgaretti (Max Planck Institute for Intelligent Systems)

100 Temperature gradient induced solvent coarsening around colloids

Using mesoscopic numerical simulations and analytical theory we investigate the coarsening of the solvent structure around a colloidal particle emerging after a temperature quench of the colloid surface. Qualitative differences in the coarsening mechanisms are found, depending on the composition of the binary liquid mixture forming the solvent and on the adsorption preferences of the colloid. For an adsorptionwise neutral colloid, as function of time the phase being next to its surface alternates. This behavior sets in on the scale of the relaxation time of the solvent and is absent for colloids with strong adsorption preferences. A Janus colloid, with a small temperature difference between its two hemispheres, reveals an asymmetric structure formation and surface enrichment around it, even if the solvent is within its one-phase region and if the temperature of the colloid is above the critical demixing temperature $T_c$ of the solvent. A comparison between the emerging fluid structures above and below $T_c$ is provided. Our phenomenological model turns out to capture recent experimental findings according to which, upon laser illumination of a Janus colloid and due to the ensuing temperature gradient between its two hemispheres, the surrounding binary liquid mixture develops a concentration gradient.

Speaker: Anna Maciolek (ICHF PAN)

10:30 Coffee break

Session 13: Closing Ceremony

Convener: Prof. Paweł Góra

101 Guessing the direction of Time's Arrow: theory and experiment

As famously articulated by Sir Arthur Eddington, the second law of thermodynamics implies a directionality to the flow of time: the arrow of time points in the direction of increasing entropy. This deep fact of Nature is something that we intuitively grasp in our everyday lives, which is why we typically find it easy to distinguish between a movie played forward in time, and one played backward. With nanoscale systems the situation becomes more subtle due to the prominence of statistical fluctuations. At sufficiently small length and time scales, a system may behave in a manner that appears contrary to the second law. Surprisingly, our ability to distinguish the direction of the arrow of time can be quantified and shown to obey a universal law. I will show how this law emerges from non-equilibrium fluctuation relations, and I will present experimental results that have verified its validity, using a driven quantum dot.

Speaker: Christopher Jarzynski (University of Maryland, College Park)

102 Eliminating ensembles from equilibrium statistical physics: Maxwell's demon, Szilard's engine, and thermodynamics via entanglement

A system in equilibrium does not evolve: time independence is its telltale characteristic. However, in Newtonian physics microstate of an individual system (a point in its phase space) evolves incessantly in accord with its equations of motion. Ensembles were introduced in XIX century to bridge that chasm between continuous motion of phase space points in Newtonian dynamics and stasis of thermodynamics: While states of individual classical system inevitably evolve, a phase space distribution of such states -- an ensemble -- can be time-independent. I show that entanglement (e.g., with the environment) can yield time-independent equilibrium in an individual quantum system. This allows one to eliminate ensembles -- an awkward stratagem introduced to reconcile thermodynamics with Newtonian mechanics -- and use individual system interacting with its heat bath to represent equilibrium and to elucidate the role of information and measurements in physics. Thus, in our quantum Universe one can practice statistical physics without ensembles. I illustrate classical difficulties and the need for ensembles with Szilard's engine, and show that in a similar quantum engine a single system entangled with the environment is enough. The role of Maxwell's demon (which in this quantum context resembles Wigner's friend) is also discussed.

Speaker: Wojciech Zurek (Los Alamos)

103 Microreversibility, current fluctuations, and entropy production in nonequilibrium systems

On the basis of microreversibility, fluctuation relations are established for the counting statistics of coupled currents flowing across classical or quantum systems sustaining nonequilibrium steady states. Thanks to these relations, the Green-Kubo formulae and the Casimir-Onsager reciprocity relations can be generalized from linear to nonlinear response properties. These advances provide a framework to formulate nonequilibrium thermodynamics in small systems. In this framework, the entropy production can be interpreted as the order parameter of time-reversal symmetry breaking at the statistical level of description. These results apply to hydrodynamic flows, driven Brownian motion, active particles, molecular motors, polymerizations, reactions, as well as to quantum transport in mesoscopic devices. $ $ [1] P. Gaspard, Multivariate fluctuation relations for currents, New J. Phys. **15** (2013) 115014. [2] P. Gaspard, Time-reversal symmetry relations for fluctuating currents in nonequilibrium systems, Acta Phys. Pol. B **44** (2013) 815. [3] P. Gaspard, Time-reversal symmetry relation for nonequilibrium flows ruled by the fluctuating Boltzmann equation, Physica A **392** (2013) 639. [4] D. Lacoste and P. Gaspard, Isometric fluctuation relations for equilibrium states with broken symmetry, Phys. Rev. Lett. **113** (2014) 240602. [5] P. Gaspard, Force-velocity relation for copolymerization processes, New J. Phys. **17** (2015) 045016.

Speaker: Pierre Gaspard (Universite Libre de Bruxelles (U.L.B.))

12:30 Lunch