Stochastic entropy production in diffusive systems

TL;DR

This paper discusses methods for calculating the distribution of stochastic entropy production in diffusive systems, highlighting recent advances that enable approximate solutions via numerical techniques, demonstrated through various examples.

Contribution

It introduces a framework using a product of positive functions to approximate the entropy production distribution in diffusion processes, applicable to higher-dimensional systems.

Findings

The framework simplifies the computation of entropy production distributions.

Numerical techniques effectively approximate solutions where analytical forms are intractable.

Examples demonstrate the method's applicability to multi-dimensional diffusion systems.

Abstract

Computing the stochastic entropy production associated with the evolution of a stochastic dynamical system is a well-established problem. In a small number of cases such as the Ornstein-Uhlenbeck process, of which we give a complete exposition, the distribution of entropy production can be obtained analytically, but in general it is much harder. A recent development in solving the Fokker-Planck equation, in which the solution is written as a product of positive functions, enables the distribution to be obtained approximately, with the assistance of simple numerical techniques. Using examples in one and higher dimension, we demonstrate how such a framework is very convenient for the computation of stochastic entropy production in diffusion processes.