Related papers: Stationarity, soft ergodicity, and entropy in rela…
We study the local entropy production rate and the local entropy flow in active systems composed of non-interacting run-and-tumble particles in a thermal bath. After providing generic time-dependend expressions, we focus on the stationary…
We study ergodic properties of one-dimensional Brownian motion with resetting. Using generic classes of statistics of times between resets, we find respectively for thin/fat tailed distributions, the normalized/non-normalised invariant…
The random walk of test particle in low-density gas is considered basing on approximate coarsened version of the collisional representation of the BBGKY equations. The coarsening presumes that momentum relaxation rates of the test particle…
As recently manifested , the quench dynamics of isolated quantum systems consisting of a finite number of particles, is characterized by an exponential spreading of wave packets in the many-body Hilbert space. This happens when the…
The non-equilibrium steady states emerging from stochastic resetting to a distribution is studied. We show that for a range of processes, the steady-state moments can be expressed as a linear combination of the moments of the distribution…
We study systems of Brownian particles on the real line, which interact by splitting the local times of collisions among themselves in an asymmetric manner. We prove the strong existence and uniqueness of such processes and identify them…
The concept of entropy has been pivotal in the formulation of thermodynamics. For systems driven away from thermal equilibrium, a comparable role is played by entropy production and dissipation. Here we provide a comprehensive picture how…
We present models for single-particle dispersion in vertical and horizontal directions of stably stratified flows. The model in the vertical direction is based on the observed Lagrangian spectrum of the vertical velocity, while the model in…
Non-equilibrium fluctuations of various stochastic variables, such as work and entropy production, have been widely discussed recently in the context of large deviations, cumulants and fluctuation relations. Typically, one looks at the…
We review theoretical models of individual motility as well as collective dynamics and pattern formation of active particles. We focus on simple models of active dynamics with a particular emphasis on nonlinear and stochastic dynamics of…
A classical particle system coupled with a thermostat driven by an external constant force reaches its steady state when the ensemble-averaged drift velocity does not vary with time. The statistical mechanics of such a system is derived…
A unifying theory is put forward that entropy is equal to action. The crowning derivation is based on information theoretic methods and uses our hypothesis that "particles move via the discrete Bernoulli Process." While this hypothesis…
Suppose that particles are randomly distributed in $\bR^d$, and they are subject to identical stochastic motion independently of each other. The Smoluchowski process describes fluctuations of the number of particles in an observation region…
Elastic confinements are an important component of many biological systems and dictate the transport properties of suspended particles under flow. In this chapter, we review the Brownian motion of a particle moving in the vicinity of a…
We investigate the properties of a model of granular matter consisting of $N$ Brownian particles on a line subject to inelastic mutual collisions. This model displays a genuine thermodynamic limit for the mean values of the energy and the…
After a brief historical survey, the paper introduces the notion of entropic model sets (cut and project sets), and, more generally, the notion of diffractive point sets with entropy. Such sets may be thought of as generalizations of…
The statistics of lagrangian velocity divergence are studied for an assembly of particles in compressible turbulence on a free surface. Under an appropriate definition of entropy, the two-dimensional lagrangian velocity divergence of a…
A thermal analogue of the classical brachistochrone problem, which minimizes the connection time between two equilibrium states of harmonically confined Brownian particles, has recently been solved theoretically. Here we report its…
Entropy estimation, due in part to its connection with mutual information, has seen considerable use in the study of time series data including causality detection and information flow. In many cases, the entropy is estimated using…
We argue that the dynamics of particle imbalance in quadratic fermionic models is, for the majority of initial many-body product states in site occupation basis, virtually indistinguishable from the dynamics of survival probabilities of…