Brownian motion is one of the most fundamental processes in non-equilibrium statistical physics. High resolution data from single particle tracking and supercomputing across the scales demonstrate deviations from the simple law of Brownian motion. I will introduce the concept of "doubly-stochastic" processes for the modelling of transport in heterogeneous systems, before turning to "anomalous...
Strong symmetries of Fractional Brownian Motion (FBM) make its Hurst index $H$ the unifying number governing both its short (fractal dimension $2-H$) and long time (mean squared displacement $\propto t^{2H}$) properties. This fact restricts some of its applications—crucially it makes it impossible to describe an increasing number of regime switching anomalous diffusion systems in which the...
The study of synchronous dynamics has traditionally focused on the identification of threshold parameter values for the transition to synchronization, and on the nature of such transition. The dynamical process whereby systems of self-sustained oscillators synchronize, however, has been much less studied. While one might reasonably expect such a process to be strongly system-dependent, in Ref....
An optimization problem can be translated into physics language as the quest for the energy minimum of a complex system with a Hamiltonian that encodes the problem itself. Stretching the analogy further, the optimization problem can be seen as the controlled cooling of such a complex system so as it lands in a minimum of its complex energy landscape corresponding to the optimal solution of the...
The Kibble-Zurek mechanism (KZM) is a theoretical framework that describes the dynamics of non-equilibrium processes and defect formation in systems undergoing second-order phase transitions.
This mechanism finds widespread application in various fields, including cosmology and condensed matter physics.
I will explore the numerical simulation of KZM using Landau-Ginzburg dynamics and its...
Many-body localization (MBL) seems to be a robust example of ergodicity breaking. While manifested in small systems and for short times (in experiment) its very existence in the thermodynamic limit has been questioned recently. I will discuss recent efforts to answer this query by various means from exact diagonalization to large systems dynamics using tensor network approaches, the role of...
The fluctuations and the response of stochastic systems are not independent but related by fluctuation-dissipation theorems or, equivalently, fluctuation-response relations (FRRs). Originally introduced for systems in thermodynamic equilibrium, generalizations of such relations for non-equilibrium situations have been discussed since the 1970's and are particularly appealing for biological...
Chemically active systems are characterized by the presence of chemical processes which convert energy from the environment to perform activity. Examples are self-propelled particles, active droplets, active gels or molecular motors. The continuous flow of energy, stemming from the chemical reactions, prevents the system to reach thermal equilibrium at molecular scales. For this reason, active...
Over the past years, the generation of interactions breaking action-reaction symmetry has emerged as new paradigm for active matter. Such nonreciprocal interactions have in particular been argued to constitute a generic route for the emergence of steady states breaking time reversal symmetry. The generalization of the Cahn-Hilliard theory of phase separation to nonreciprocal mixtures predicts,...
Rare events, although infrequently occurring, can have significant consequences in various fields such as epidemics, ecological dynamics, biological switches, chemical reactions, and natural disasters. Existing techniques like the Wentzel-Kramers-Brillouin (WKB) method and transition path sampling algorithms provide insights into rare event paths, but they have limitations. The WKB method only...
Understanding how information is transmitted from the exterior to the interior of living cells is essential for developing new therapeutic strategies. Despite recent structural advances, the mechanisms that govern interactions of membrane-bound receptors with intracellular arrestin molecules at the plasma membrane remain elusive. Here [1], we combine single-molecule microscopy with molecular...
First-passage phenomena are ubiquitous in nature and at the heart of e.g., reaction kinetics, gene regulation, the foraging behavior of animals, and stock option dynamics. Whereas theoretical studies focus on predicting statistics of the first-passage time for a given process, practical applications typically aim at inferring kinetic rates, i.e. inverse mean first-passage times, from...
Many machine learning (ML) algorithms require complete knowledge of the hardware in which they run. They also require detailed control of the hardware physical properties.
Reservoir Computing (RC) is a ML algorithm that can be implemented with minimal control of the physical properties of the hardware. In RC, a non-linear dynamical system acts as a generator of an infinite features...
Noise can significantly impact Machine Learning performance, both in real-world data and due to adversarial attacks. Our method aims to mitigate the effect of noise by introducing data abstractions, which reduce the impact of noise but may result in some loss of information and accuracy. The poster explores various approaches to abstractions for numerical data and binary classification tasks....
The continuum field theoretic approach to describing a many-particle system has been very useful in understanding its thermodynamic and time-dependent behaviour. Our discussion will be on the fluctuating hydrodynamic description used to study the behaviour of a system of passive systems and the active matter of self-propelled particles. The dynamics are primarily formulated in terms of a set...
There has been a lot of interest in nanoscale devices that can mimic some brain functionalities. In this talk, we discuss
mean field theoretical techniques that can be used to study nanoscale devices with memory, including recent experiments on self-organizing nanowires. A large body of work has shown that PVP-coated self-organizing Ag nanowires have a dynamic response to an applied voltage...
Two models in which dynamic conductance is modelled as an overdamped motion in a potential, display memristive behavior and stochastic resonance when subject to an external noise. One is a tilted two-well potential and the other a monostable well but with both additive and mutiplicative noises.
I prove global in time existence of solutions to the full revised Enskog equation. This equation generalizes the Boltzmann theory to dense gases in two ways:
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by taking into account the fact that the centers of two colliding spheres are at a distance a, equal to the diameter of hard spheres.
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by increasing the collision frequency by a factor $Y_0$ which nowadays is identified with...
Resetting a stochastic process has been shown to expedite the completion time of some complex tasks, such as finding a target for the first time. In this talk we consider the cost of resetting by associating a cost to each reset, which is a function of the
distance travelled during the reset event.
We show some unexpected results. First, in the limit of a vanishing resetting rate, the mean...
A system with long range interaction (LRI) is usually characterized by a non-extensive energy. While, by properly scaling the Hamiltonian of the system, the energy can become extensive, it may still suffer from non-additivity. In other words, such a system with volume $V$ and (rescaled) energy $E$, cannot be divided into two subsystems with energies $E_1,E_2$, where $E = E_1 + E_2 +...
The entropy production of an open system coupled to a reservoir initialized in a canonical state can be expressed as a sum of two microscopic information-theoretic contributions: the system-bath mutual information and the relative entropy measuring the displacement of the environment from equilibrium. We investigate whether this result can be generalized to situations where the reservoir is...
According to conventional wisdom, a macroscopic system placed in an environment with a different temperature relaxes to the temperature of the surroundings, mediated by the flow of heat that is set only by the instantaneous temperature difference. However, when rapid changes in temperature push a system far from thermodynamic equilibrium, thermal relaxation becomes asymmetric. That is, under...
Stochastic Thermodynamics usually investigates and describes Markovian systems where memory is absent. A typical example is Brownian Motion, where dynamics are overdamped with a delta-correlated noise term. Yet this Markovian hypothesis is very strong, and only valid for a limited range of time and length scales. More generally, a wide range of physical systems exhibit memory with finite...
Optimal protocols have been a subject of intense research in stochastic thermodynamics due to their importance for the understanding of biological processes and the operation of heat engines at the micro- and nanoscale. In this study, we experimentally investigate protocols to transport a Brownian particle over a given distance within a finite time using an optical trap that minimize the work...
TBA
Understanding transport processes through membranes require the modeling of diffusion, particularly when it comes to enhancing process effectiveness. The goal of this research is to understand the relationship between membrane structures, external forces, and the characteristic features of diffusive transport. We investigate Cauchy flight diffusion with drift in heterogeneous membrane-like...
We discuss the impact of polydispersity on particle currents generated by Brownian hard spheres when they are driven through periodic potentials by a constant drag force. Considering random mixtures of two types of spheres, we explain the variation of the currents with the mixing ratio of the two components and with the hard-sphere diameters. A basic unit cell exists in the space of the two...
We reinvestigate a paradigmatic model of nonequilibrium statistical physics consisting of an inertial Brownian particle in a symmetric periodic potential subjected to both a time-periodic force and a static bias. In doing so we focus on the negative mobility phenomenon in which the average velocity of the particle is opposite to the constant force acting on it. Surprisingly, we find that in...
Investigation of non-equilibrium fermionic transport in a periodically-driven tilted lattice is currently a subject of major interest. Transport properties in this setting are influenced by the drive, tilt, and interactions, as well as the non-Markovian nature of the fermionic reservoirs. We address this setup with two complementary tools, with an ultimate aim at addressing the interplay of...
Recent developments in experimental condensed matter physics allow for realization of Abelian gauge Hamiltonians on routinely controllable systems (Josephson junction arrays, optical lattices, etc). This opened the prospect of simulation of the phenomena of compact quantum electrodynamics and quantum chromodynamics (e.g, quark confinement) in the laboratory setup.
We consider $Z_N$ symmetric...
To describe the growth of a cell colony, processes such as cell division, cell death and cell movement must be taken into account. All of these mechanisms can have multiple contributing factors, and one of them is the density of cells in the surroundings.
It is often assumed that the growth of cancer cell colonies is characterized by an exponential increase in the number of cells, and a...
Biological systems ranging from cytoskeletal networks to bacterial suspensions and epithelial monolayers exhibit complex chaotic flows known as active turbulence. Countless active molecular interactions combine to form a turbulent mix of behaviours, with fascinating non-equilibrium properties. With an eye to developing a quantitative understanding, we study turbulence and spatiotemporal chaos...
Knotted proteins can become jammed when forced through pores if the knots in their backbone tighten under force. Alternatively, the knot can slide off the chain, enabling translocation. This process can be described using a simple energy landscape model with a time-periodic potential that mimics the action of a molecular motor. Such a stochastic model exhibits similar behaviour to results...
Active nematics are active fluids composed of elongated constituents in which force dipoles at the micro scale generate macroscopic flows. As in other active systems, bulk active nematics exhibit chaotic flows known as active turbulence. Unique to active nematics, however, is the existence of local orienational order, allowing the prescription of topological defects from various boundary...
In this work we study the problem of a random walk
in a finite-size randomly inhomogeneous one-dimensional medium by using a Fock space approach.
We map the master equation of the walker into a Schr\"odinger-like equation
and we describe the evolution of the random walk in a Fock space in which the
system states are assigned to the sites of a regular one-dimensional lattice.
This...
Patterns arise in nature at different scales. We can recognize animals based on their furry patterns alone, from the spots on a leopard to the stains on a cow. However, patterns are established also during embryonic development, through interactions of diffusing molecules that activate expression of target genes. As a result a striped pattern of gene expression emerges. These stripes will...
We present general results on fluctuations and spatial correlations of the coarse-grained empirical density and current of diffusion on all time scales in equilibrium or non-equilibrium steady states [1,2] and for transient or non-ergodic dynamics [3]. The time averaging and coarse graining hardwired in the definition of the functionals under consideration give rise to experimentally relevant...
We investigate the anomalous kinetics of two-species reaction-diffusion system $A+A \rightarrow (\emptyset, A)$, $A+B \rightarrow A$ near its upper critical dimension $d_c = 2$. In particular, we analyze an advection of reactants by random velocity field generated by the stochastically forced Navier-Stokes equation. The model is analysed by means of field-theoretic renormalization group (RG)...
Magnetohydrodynamic (MHD) turbulence driven by the stochastic Navier-Stokes equation always has been a subject of intense study. In an electrically conducting media developed turbulence has a number of specific properties associated with magnetic field fluctuations which under certain conditions can increase and lead to the formation of a non-zero average large-scale magnetic field. This...
Often the motion in complex systems is subdiffusive. Meaning, instead of a linear dependence on time, the mean square displacement (MSD) grows as $\sim t^\alpha$ where $0 < \alpha < 1$. This can be attributed to long waiting times that cause a significant slowdown from the classical description of Brownian motion. But a slow down of the MSD can also arise from repeated collisions with...
Slow compression of a hard-sphere fuid at constant temperature yields an entropy-driven first-order transition from the liquid to a crystalline phase [1, 2]. When the fuid is compressed quickly rather than slowly, however, crystallization can be avoided and the particles "jam" in a disordered configuration. The determination of the so-called random close packing (RCP) density, defined as the...
Classical measuring methods used in material engineering are not suited for biological tissues, especially in microscale. It is almost impossible to produce a homogenous specimen of biological material for a classical tensile test. Indentation experiments are much easier to perform on a microscopic object like a cell. However, this comes at a cost: interpretation of the results. Extracting...
Engines powered by active particles are well-known for their exceptionally high performance: their efficiency can surpass the Carnot efficiency while simultaneously achieving positive power. However, this 'super-Carnot' behavior arises from considering the apparent statistical signature of the system as a whole, without distinguishing heat and work.
Consequently, this ‘apparent’ description...
Active work quantifies the amount of energy converted into the actual motion of active particles. In the long-time limit, the time-averaged active work quantifies how much energy is dissipated by active particles into the surrounding environment, i.e., it is a measure of the entropy production rate of active particles. Thus, by calculating the large deviation function (LDF) of the...
The effective dynamics of stochastic systems with a finite number of states where only a few degrees of freedom are accessible to observation is described in terms of coarse-grained models. Coarse graining on states typically entails non-markovianity that is recovered under physically motivated assumption, thus restricting the range of applicability of such models. We use a novel approach...
Understanding the role of active fluctuations in physics is a problem emerging both as a hot topic and a major challenge. The reason for this is their inherent non-equilibrium nature. This feature opens a landscape of phenomena yet to be explored that are absent in the presence of thermal fluctuations alone. Recently a paradoxical effect has been briefly communicated in which a free particle...
A major challenge in soft matter physics is to understand the repercussions of an external shear flow on the microscopic structure of colloidal suspensions. In the case of diluted suspensions of spherical colloids, a common starting point for the theoretical treatment of the problem is the two-body Smoluchowski convection-diffusion equation [1]. However, solving the latter equation is...
We present two approaches to explore the dynamics of many-body localization (MBL) in disordered interacting quantum systems using experimentally measurable single- and two-site correlation functions.
First [1], we propose an algorithm based on neural networks that uses two-site correlation functions to detect ergodic bubbles, i.e., delocalized regions surrounded by a localized phase, with a...
We studied random sequential adsorption packings constructed from rectangles,
ellipses, and discorectangles, where the orientations of constituent shapes were
picked from discrete sets of values with varying spacing. It allowed us to monitor
the transition between the two edge cases: the parallel alignment and the arbitrary, continuous orientation of the shapes within the packing. The...
Among the soft matter systems one finds crystalline and liquid crystalline structures, but in the meantime also quasicrystalline. These can have fivefold or more than sixfold symmetries, which are not compatible with translational symmetry. Model structures are tesselations with more than one tile subdued to matching rules, or projections from higher dimensional periodic crystals. The higher...
The Family-Vicsek relation [1] is a seminal universal relation obtained for the global roughness at the interface of two media in the growth process. In this Letter, we revisit the scaling analysis and, through both analytical and computational means, show that the Family-Vicsek relation can be generalized to a new scaling independent of the lateral size, substrate dimension $d$, and scaling...
In this talk I will present my memories of a four-decade long connection, both professional and personal with Professor Lech Longa. I will focus on the primary ways this connection developed and grew: visits I made to the Jagiellonian University, visits he made to Kent State University (including a year-long Fulbright Fellowship), and two sets of biennial conferences we both attended, namely...
The discovery of the twist-bend nematic phase (NTB) can be considered as one of the most significant recent achivements in the field of liquid crystals. In the NTB phase the director is tilted at constant angle θ and forms a heliconical structure with nanoscale pitch which appears despite the achiral structure of the constituent molecules. From the general soft matter point of view the NTB...
Confined nematic liquid crystals are characterized by the interplay of ordering, elasticity, chirality, confinement, surface anchoring, external fields, flows, and activity that leads to numerous complex static and dynamic structures, including singular topological defects and nonsingular solitonic deformations. Increasing interest in active soft matter stimulated us to analyze topological...
The elastic behaviour of nematic liquid crystals is commonly interpreted on the basis of the Oseen-Frank free energy [1,2], in which the cost for distortions from the uniform alignment is decomposed into contributions corresponding to three modes – splay, twist, and bend - built from the first-order derivatives of the position dependent director. Typical low molecular mass thermotropic systems...
Active systems refer to collections of entities that consume energy and thereby move forward showing emergent collective dynamics. In the macroscopic world this could be fish schools or flocks of birds. In the microscopic world, which we address here, the entities often have the shape of rods like bacteria or are flexible filaments such as microtubules, which are biopolymers found within...
Assemblies of hard ellipsoidal particles form orientationally ordered phases with increasing number density. A simple self-consistent mean field model is proposed to study the transition from the isotropic to the nematic phase. The simplicity of the model gives ready access to the order parameter, free energy and pressure, in good agreement with simulations. The model may be useful to describe...
Bent-core liquid crystals are mesophases formed by molecules having a "banana-like" shape that favors spontaneous bend deformations in the nematic director field. As a pure bend deformation cannot uniformly fill 3D space, Meyer and later independently Dozov argued that these local bend deformations should be accompanied by either a twist or a splay deformation [1]. In the former case, they...
From European Social Survey 2012-2016, data are selected on how Polish respondents are attached to 21 issues. The list of issues is formulated according to the scheme: 'it is important to ...' and it includes items like: try new and different things, make own decisions, seek fun, follow traditions, behave properly etc.
The answers are weighted according to 6-point Likert scale. The Pearson...
Understanding vehicular dynamics in urban areas is a central task for modifying urban space planning and implementing effective policies to optimize transportation time and reduce carbon dioxide emissions. Incorporating parking slots is crucial as parking maneuvers and cruising for parking impact vehicular flow. From a microscopic perspective, vehicular traffic can be treated as interacting...
We analyze pros and cons of the recently introduced theoretical framework, within which the dynamics of nonequilibrium diffusion processes is related to the fully Euclidean version of the Schr\"{o}dinger quantum mechanics with a minimal electromagnetic coupling. The arising "magnetic" affinity is set against the standard theory of the Brownian motion in a magnetic field. The benefit is...
Diffusion of particles in random, correlated diffusivity landscapes can serve as one of the models leading to the so-called Brownian yet non-Gaussian diffusion. Under the corresponding choice of parameters, the model leads to the mean squared displacement of particles growing linearly in time, with the probability density function (PDF) of displacements changing its shape from a double-sided...
We study the statistics of a one-dimensional randomly advected field with diffusion. The motivation for this setup comes from a straightforward interpretation as advection of particles in one-dimensional turbulence, but it is also related to a problem of synchronization of dynamical systems driven by common noise. A general class of lattice models describing the joint effect of random...
The study of the dynamics of occupation time has a variety of applications. For ex-
ample, it has been used to analyze the morphological dynamics of interfaces, analysis
of the fluorescence intermittency emitting from colloidal semiconductor dots, optical
imaging etc to name a few. The occupation time dynamics have been studied for
numerous problems in the context of non-equilibrium...
With this talk I attempt to give an overview of the present state of thermodynamics/statistical mechanics of systems of finite size and/or small scales where quantum features matter. I will survey the present state of what I think is more or less settled and what are the main (open) problems and issues that still hunt this timely area of research on a classical level -- and even more...
