We consider quantum dynamics on a graph, with repeated strong measurements performed locally at a fixed time interval $\tau$. For example a particle starting on node $x$ and measurements performed on another node $x'$. From the basic postulates of quantum mechanics the string of measurements yields a sequence no,no,no, $\cdots$ and finally in the $n$th attempt a yes, i.e. the particle is...
Evolving stochastic process, when interrupted at random epochs and reset to its initial condition, reaches a new nonequilibrium stationary state. The approach to the stationary state is accompanied by an unusual `dynamical phase transition'. Moreever, the mean firstpassage time to a fixed target becomes a minimum at an optimal value of the resetting rate. This makes the diffusive search...
In this work we consider the role of active inclusions in a growing interface, for example membrane binding proteins which catalyse growth in the plasma membrane of eukaryotic cells. The interface is thus rendered active and is described by two coupled fields: the height field of the interface and the density of the inclusions. The equations generalise to active interface growth the Kardar...
We analyze a couple of simple systems, without stationary probability distribution, in order to show how to proceed for obtaining detailed as well as integral fluctuation theorems in such a kind of systems. To reach such a goal, we exploit a path integral approach that adequately fits to this kind of study. This methodology, together with the variational approach, are also exploited to...
The treatment of cancer by boosting the immune system is a recent and promising therapeutic strategy. During interactions, the immune system cells learn to recognize cancer cells. Analogously, the cancer cells can develop the ability to blend into the surrounding tissue and mislead the immune system cells.
I will present a model of cell interactions in the framework of thermostatted kinetic...
We calculate the timedependent probability distribution function (PDF) of an overdamped Brownian particle moving in a onedimensional periodic potential energy $U(x)$. The PDF is found by solving the corresponding Smoluchowski diffusion equation. We derive the solution for any periodic even function $U(x)$ and demonstrate that it is asymptotically (at large times $t$) correct up to terms...
In this talk, we explore an approach to understanding price fluctuations within a market via considerations of functional dependencies between asset prices. Interestingly, this approach suggests a class of models of a type used earlier to describe the dynamics of real and artificial neural networks. Statistical physics approaches turn out to be suitable for an analysis of their collective...
A considerable number of systems have recently been reported in which Brownian yet nonGaussian dynamics was observed. These are processes characterised by a linear growth in time of the mean squared displacement, yet the probability density function of the particle displacement is distinctly nonGaussian, and often of exponential (Laplace) shape. This behaviour has been interpreted as...
Chemical processes in closed systems inevitably relax to equilibrium. Living systems avoid this fate and give rise to a much richer diversity of phenomena by operating under nonequilibrium conditions. Recent experiments in dissipative selfassembly also demonstrated that by opening reaction vessels and steering certain concentrations, an ocean of opportunities for artificial synthesis and...
The sensitivity to perturbations of the Fisher, Kolmogorov, Petrovskii, and Piskunov (FKPP) wave front is used to find a quantity revealing the perturbation of diffusion in a concentrated solution. We consider two chemical species A and B engaged in the reaction A + B $\rightarrow$ 2A. When A and B have different diffusivities $D_A$ and $D_B$, the deterministic dynamics includes...
Quantum analogs of classical random walks have been defined in quantum information theory as a useful concept to implement algorithms. Due to interference effects, statistical properties of quantum walks can drastically differ from their classical counterparts, leading to much faster computations.
We shall present various statistical properties of continuoustime quantum walks on a ...
The classical firstpassage theory for random walks is generalized to quantum systems by using repeated attempts with a fixed frequency $1/\tau$ to find the system in the detection state $ \psi_\text{d}\rangle$. The first successful of these attempts defines the time $T = N \tau$ of first detected arrival. Here, the Zeno limit $\tau\to0$ of diverging detection frequency is investigated. The...
The model of a step quantum heat engine (SQHE) is defined as a working body, given by the twolevel system (TLS), acting separately (i.e. in steps) with the heat baths and the energy storage system (a battery). A single step of the engine is defined as the unitary and energy conserving operation. For the general SQHE we prove the fundamental attainable efficiency, given as a function of a cold...
The development of multicellular organisms is a dynamic process in which cells divide, rearrange, and interpret molecular signals to adopt specific cell fates. Despite the intrinsic stochasticity of cellular events, the cells identify their position within the tissue with striking precision of one cell diameter in fruit fly or three cell diameters in vertebrate spinal cord. How do cells...
The EliazarKlafter targeted stochasticity concept , together and that of the reverse engineering (reconstruction of the stochastic process once a target pdf is a priori given), has been originally devised for Lévydriven Langevin systems. Its generalization, discussed in [PRE 84, 011142, (2011)], involves a nonLangevin alternative which associates with the sam Levy driver and the same...
The Levy walk processes with rests restricted to a region bounded by two absorbing barriers are discussed. The waiting time between the jumps is given by an exponential distribution with a constant jumping rate and with a positiondependent jumping rate. The time of flight for both ranges of $\alpha$: lower $(0,1)$ and higher $(1,2)$, is considered.
For constant jumping rate two limits are...
I will present the solutions of Volterra equations with the fading memory given by the Prabhakar function with negative upper parameter which is relevant to the standard nonDebye models of dielectric relaxation, namely for the ColeCole, ColeDavidson, and HavriliakNegami models. These integrodifferential equations are solved by using the umbral calculus and Laplace transform method whose...
Although there is not a complete “proof” of the second law of thermodynamics based on microscopic dynamics, two properties of Hamiltonian systems have been used to prove the impossibility of work extraction from a single thermal reservoir: Liouville’s theorem and the adiabatic invariance of the volume enclosed by an energy shell (Helmholtz's theorem). In this talk, I will review these two...
We show that the entropy production in small open systems coupled to environments made of extended baths is predominantly caused by the displacement of the environment from equilibrium rather than, as often assumed, the mutual information between the system and the environment. The latter contribution is strongly bounded from above by the ArakiLieb inequality, and therefore is not...
Transitions to chaos have been previously extensively studied in different setups of randomly connected networks. The prevailing assumption is that, due to the central limit theorem, synaptic input can be modeled as a Gaussian random variable. In this scenario, a continuous transition has been found in rate models with smooth activation functions. However, these models do not take into account...
A $q$neighbor majorityvote model for the opinion formation is introduced in which agents
represented by twostate spins update their opinions on the basis of the opinions of
randomly chosen subsets of $q$ their neighbors ($q$lobbies). The agents with probability
$(12p)$, $0\le p\le1/2$, obey the majorityvote
rule in which the probability of the opinion flip depends only on the sign of...
Currently, the investigations of resistive switching have attracted much attention. Electronic devices, the functioning of which is based on the resistive switching, are called memristors. The memristor as a new fundamental element of the electrical circuit that dissipates energy and has memory was theoretically predicted by Chua in 1971, but found its hardware implementation only in 2008. It...
Enormous progress in machine learning achievements, going together with their excellent implementations on userfriendly platforms, have pushed many of us towards this
methodology. Can we get better explanations for studied data? Can we get the explanation easier? In the following we deal with data formed from recordings on healthy people with different age and sex. The problem is how the age...
Singleparticle trajectories measured in microscopy experiments contain important information about dynamic processes undergoing in a range of materials including living cells and tissues. However, extracting that information is not a trivial task due to the stochastic nature of particles’ movement and the sampling noise. It usually starts with the detection of a corresponding motion type of a...
We study a system which consists of two media divided by a thin partially permeable membrane. One of these media is diffusive. The second one is subdiffusive. Moreover, transported particles can be absorbed in the subdiffusive medium. In order to find methematical description of a transport process we use a new, universal model that is presented in details in \textit{T. Koszto\l{}owicz, Phys....
We investigate an adaptive network model describing human smoking behavior incorporating the social processes homophily and induction introduced by Schleussner et al. (Sci Rep 2016). Upon social transition, the smoking prevalence in the model decreases, leaving remaining smokers clustered and marginalized in the network. Intriguingly, the model qualitatively resembles empirical findings....
Continuoustime random walk (CTRW) is a stochastic process with continuous and fluctuating waiting (interevent) time. It was first introduced to physics by Montroll and Weiss. Since then it has been used in many areas of science [1]. CTRW is also successfully applied in econophysics [2], for example, it is used to describe stock price dynamics. We can consider the stock price as the price of...
Using a new method, time evolution of the probability distribution of the number of particle passes through a thin membrane will be derived. As far as we know, a distribution of the number of particle's passes between selected points of the system (membrane surfaces) have not been determined yet.
We assume that a passage of a particle through the membrane may cause a change in particle's state...
Hard objects can behave differently from the objects/particles that are interacting through soft potential. The main difference is that soft interacting particles can store potential energy accomodating at the same time their positions. Hard interacting particles possess no potential energy and their arrangement is fully according to the entropic and geometry conditions. The excluded volume...
The structural relaxation of dense liquids displays a drastic slowing down upon compression or cooling, a phenomenon which is commonly identified with the glass transition. Many dynamical properties of the glass transition in bulk liquids have been successfully described by modecoupling theory (MCT [1]). Even more involved is the description of confined liquids since they already exhibit...
Technological applications of liquid crystals (LC) have been for many decades a continous driving force for investigating properties of this fascinating state of matter by theorists as well as by experimentalists. Still many questions about LC properties need to be answered. Special attention is paid to the optical characteristics of liquid crystalline thin films. In the current...
The passage of long biochemical structures through nanochannels from one side to the other side of a membrane is a normal process in biology. Drug absorption, protein and DNA/RNA passage through cell membranes and nuclear pores, DNA packaging by phage viruses are a few known examples.
After Kasianowick work on 1996, both theoretical and experimental investigations have been developed to...
This work aims to create prototype structures of hybrid polymeric membranes with the desired quantity, size and distribution of obstacles, which corresponds to the given amount of magnetite in the hybrid alginate membrane. The membrane is represented by a black and white image where the black regions corresponds to polymer matrix and are available for diffusive particles and the white ones are...
Bentshaped particles gain more and more interest nowadays
due to the formation of novel liquid crystalline structures. Here, we investigate impact of molecular shape and conformational degrees of freedom on stabilization of nematic phases in two dimensional systems. Analyzed particles are composed of two and three arms built of either hard disks or hard needles. Additionally, they have...
Biological molecular machines are enzymes that simultaneously catalyze
two processes, one donating free energy and second accepting it. Recent
studies show that most native protein enzymes have a rich stochastic dynamics
that often manifests in fluctuating rates of the calatyzed processes and
the presence of shortterm memory resulting from transient nonergodicity.
For such dynamics, we prove...
We report on a new kinetic equation for an auxiliary twoparticle distribution function
$f({\bf k_1}, {\bf v_1}, {\bf k_2}, {\bf v_2}, t)$.
Its general form reads
\begin{equation}
\begin{array}{l}
\displaystyle
\left(\frac{\partial}{\partial t} \, + \, {\rm i} \, {\bf k_1} {v_1} \, + \, {\rm i} \ {\bf k_2} {v_2} \right)
f({\bf k_1}, {\bf v_1}, {\bf k_2}, {\bf v_2}, t) \, = ...
Selective imaging is a challenge in Biology. OutofPhase Imaging after Optical Modulation (OPIOM) [1] exploits reversibly photoswitchable fluorophores to selectively detect a target species in the presence of spectrally interfering fluorescent species. The method combines optimized periodic illumination and phasesensitive detection, which matches the dynamics of the targeted photoreactive...
Cell’s mechanical and physical properties such as elasticity or adhesion are significant parameters determining cell behaviour [1].
Changes in mechanical properties of cells can be connected with diseases such as cancer or blood diseases. Quantification of mechanical properties, analysis and comparison of collected data, can allow understanding the mechanism of disease formation and...
Binary mixtures, i.e. the systems composed of two different species of particles, exhibit a huge variety of dynamical modes and phase transitions. This includes demixing effects and several combinations of mobility and arrest, e.g. the collective critical slowdown of the bigger particles mediated by the presence of the smaller molecules. It was recently realized that the interactions in such...
We develop an extended multifractal analysis based on the LegendreFenchel transform (some times referred to as Legendre multibranched one) rather than the routinely used canonical Legendre transform. In our variant of coarsegraining preprocessing, the local detrending of time series has been replaced by an appropriate averaging over days combined with properlysuited detrending on a daily...
Stationary states for a particle moving in a singlewell, steeper than parabolic, potential driven by Lévy noise can be bimodal. We explore in details conditions required to induce multimodal stationary states with a modality higher than two and provide phenomenological arguments determining necessary conditions for emergence of stationary states with an anticipated multimodality. The poster...
Reaction currents in chemical networks can decrease when increasing their driving affinities. Such negative differential response (NDR), a hallmark of nonequilibrium physics, is found in reaction schemes of major biological relevance, namely, substrate inhibition and autocatalysis. We display it by deriving the full counting statistics of two minimal representative models by large deviation...
The FokkerPlanck equation provides complete statistical description of a particle undergoing random motion in a solvent. In the presence of Lorentz force due to an external magnetic field, the FokkerPlanck equation picks up a tensorial coefficient, which reflects the anisotropy of the particle motion. This tensor, however, can not be interpreted as a diffusion tensor; there are antisymmetric...
Polymers are a group of molecules that presents various physicochemical properties. Some of these properties result from specific chemical groups in the polymer. Another properties are universal, they result from the fact of the chain structure of the molecule. To describe these universal properties of polymers, there are coarsegrained models, which represents this molecule as a chain. Such...
Classical option pricing schemes assume that the value of a financial asset follows a geometric Brownian motion (GBM). However, a growing body of studies suggest that a simple GBM trajectory is not an adequate representation for the dynamics of an asset due to the fattailed properties found in empirical distributions of the asset returns. To capture this phenomenon three approaches have been...
Anderson localization (AL), the absence of diffusion, is one of the most famous phenomena occurring in disordered systems. Since the original Anderson’s paper [1], AL was thoroughly investigated theoretically and observed in numerous experimental setups including light, classical waves and quantum systems. Presence of localization leads to many surprising phenomena. One of them is the *quantum...
Random sequential adsorption (RSA) is a protocol to generate random packing in the following way:

a virtual particle position and orientation in case of anisotropic shapes is selected randomly inside the packing;

if the virtual particle does not intersect with any object on the plane, it is added to the packing. Otherwise, it is removed from the system and abandoned.
One of is's key...
The role of thermal fluctuations is crucial in certain important biological processes, such as, transcription, translation, replication mechanisms, as they take place in very small scale systems.
We propose paradigmatic models for the transcription, i.e., DNA to mRNA formation and DNA replication to see the effect of the environment on these important biological processes. We consider these...
The problem of packing objects into limited space has an ancient history and is still of great importance from both utilitarian and fundamental point of view. Threedimensional random packings are especially important due to their potential application in a granular matter and life sciences, while twodimensional packings can, for example, model adsorption monolayers. These packings are...
In this presentation, we discuss the possible generalizations of the social influence with recurrent mobility (SIRM) model [Phys. Rev. Lett. 112, 158701 (2014)]. Although the SIRM model worked approximately satisfying when U.S. election was modeled, it has its limits: it has been developed only for twoparty systems and can lead to unphysical behavior when one of the parties has extreme vote...
This work presents the spectral analysis of electromyography. Electromyographic studies are used to aid in the management and diagnostic of myopathy and neuropathy disease. Using signal analysis techniques to determine the distribution of power into frequency components we indicate that there are significant differences between patients proven healthy, and patients with the myopathy or...
When studying packings of objects one observes the depencence of packing density on various factors, the symmetry of particles included. For example, the packings of ellipsoids can be denser than the packings of spheres, which represents the general trend in a transition between two continuous symmetries. Here, our main goal was to check, whether a similar effect can be observed for shapes of...
I will address the problem of computing dynamic correlation functions in Integrable QFT’s at finite temperature and out of equilibrium. The approach is based on the formfactor expansion of the correlation functions. Thanks to the integrability, the formfactors at finite temperature can be effectively bootstrapped, through a procedure generalizing the Smirnov’s bootstrap program for vacuum...
Dispersive transport of photoinjected carriers in arrays of vertically aligned fractal nanowires is considered. The conditions of the timeofflight experiment are assumed. Photocurrent response after injection of nonequilibrium carriers by the short light pulse is studied. Carriers are injected instantaneously from the left side of the array, then, move along wires under the action of a...
We are investigating a conformational entropy of mucin protein to discern its correlation with the viscoelastic properties of the biopolymer system in various thermodynamic conditions. The mucin is believed to be responsible for gel formation inside synovial fluid of joints system which is very sensitive on both temperature and concentration changes[1]. The conformational entropy is computed...
Twistbend nematic $\left(N_\text{TB}\right)$ [1, 2] is a fifth member of the nematic family, beyond uniaxial $\left(N_\text{U}\right)$ and biaxial $\left(N_\text{B}\right)$ nematics, cholesteric $\left(N^{\ast}\right)$ and blue phases $\left(\text{BP}\right)$. Its uniqueness arises from a double degenerate groundstate (ambidextrous chirality) with a periodically modulated heliconical...