Related papers: Time evolution of entropy associated with diffusiv…
This paper uses dynamical invariants to describe the evolution of collisionless systems subject to time-dependent gravitational forces without resorting to maximum-entropy probabilities. We show that collisionless relaxation can be viewed…
In many situations, the combined effect of advection and diffusion greatly increases the rate of convergence to equilibrium -- a phenomenon known as enhanced dissipation. Here we study the situation where the advecting velocity field…
We show that the number of renewals up to time $t$ exhibits distributional fluctuations as $t\to\infty$ if the underlying lifetimes increase at an exponential rate in a distributional sense. This provides a probabilistic explanation for the…
Consider a reflected jump-diffusion on the positive half-line. Assume it is stochastically ordered. We apply the theory of Lyapunov functions and find explicit estimates for the rate of exponential convergence to the stationary…
Diffusion in an evolving environment is studied by continuos-time Monte Carlo simulations. Diffusion is modelled by continuos-time random walkers on a lattice, in a dynamic environment provided by bubbles between two one-dimensional…
We consider the linear growth-fragmentation equation arising in the modelling of cell division or polymerisation processes. For constant coefficients, we prove that the dynamics converges to the steady state with an exponential rate. The…
We study the dissipation enhancement by cellular flows. Previous work by Iyer, Xu, and Zlato\v{s} produces a family of cellular flows that can enhance dissipation by an arbitrarily large amount. We improve this result by providing…
A positive rate of entropy production at steady state is a distinctive feature of truly non-equilibrium processes. Exact results, while being often limited to simple models, offer a unique opportunity to explore the thermodynamic features…
The nature of diffusion is usually studied for particles or time-evolving systems. Similar in principle, such studies can be conducted by tracking how a given function of observable properties evolves over time-akin to the evolution of…
We propose a new approximation-technique to deal with the exact macroscopic integro-differential evolution equations of statistical systems which self-consistently accounts for dissipative effects. Concentrating on one and two point…
The diffusion approximation to the relaxation on the distorted Fermi surface in a Fermi liquid is considered. The dependence of the relaxation time on the multipolarity of a Fermi surface deformation is established. The time evolution of…
We prove a central limit theorem for the momentum distribution of a particle undergoing an unbiased spatially periodic random forcing at exponentially distributed times without friction. The start is a linear Boltzmann equation for the…
Cells generally change their internal state to adapt to an environmental change, and accordingly evolve in response to the new conditions. This process involves phenotypic changes that occur over several different time scales, ranging from…
Maximum entropy reinforcement learning (MaxEnt-RL) has become the standard approach to RL due to its beneficial exploration properties. Traditionally, policies are parameterized using Gaussian distributions, which significantly limits their…
The evolution of entropy is derived with respect to dynamical systems. For a stochastic system, its relative entropy $D$ evolves in accordance with the second law of thermodynamics; its absolute entropy $H$ may also be so, provided that the…
Extracting governing physical laws from computational or experimental data is crucial across various fields such as fluid dynamics and plasma physics. Many of those physical laws are dissipative due to fluid viscosity or plasma collisions.…
The Fourier transform is often used to connect the Lorentzian energy distribution for resonance scattering to the exponential time dependence for decaying states. However, to apply the Fourier transform, one has to bend the rules of…
We find numerically that the sample to sample fluctuation of the entropy, $\Delta S$, is a tool more sensitive in distinguishing how from high temperature behaviors, than the corresponding fluctuation in the free energy. In 1+1 dimensions…
We present a position Langevin equation for overdamped particle motion on rough two-dimensional surfaces. A Brownian Dynamics algorithm is suggested to evolve this equation numerically, allowing for the prediction of effective (projected)…
We study the stochastic behavior of heterogeneous diffusion processes with the power-law dependence $D(x)\sim|x|^{\alpha}$ of the generalized diffusion coefficient encompassing sub- and superdiffusive anomalous diffusion. Based on…