Entropy production from stochastic dynamics in discrete full phase space

TL;DR

This paper analyzes the different components of stochastic entropy production in discrete phase space systems, highlighting the role of time-reversal asymmetry and nonequilibrium constraints in entropy generation.

Contribution

It introduces a detailed decomposition of entropy production components in discrete phase space models, emphasizing the third component related to phase space sign changes and asymmetry.

Findings

Third entropy component exists with phase space sign change and asymmetry

Entropy production depends on the level of model detail

Illustrated with simple particle drift and diffusion models

Abstract

The stochastic entropy generated during the evolution of a system interacting with an environment may be separated into three components, but only two of these have a non-negative mean. The third component of entropy production is associated with the relaxation of the system probability distribution towards a stationary state and with nonequilibrium constraints within the dynamics that break detailed balance. It exists when at least some of the coordinates of the system phase space change sign under time reversal, and when the stationary state is asymmetric in these coordinates. We illustrate the various components of entropy production, both in detail for particular trajectories and in the mean, using simple systems defined on a discrete phase space of spatial and velocity coordinates. These models capture features of the drift and diffusion of a particle in a physical system, including the processes of injection and removal and the effect of a temperature gradient. The examples demonstrate how entropy production in stochastic thermodynamics depends on the detail that is included in a model of the dynamics of a process. Entropy production from such a perspective is a measure of the failure of such models to meet Loschmidt's expectation of dynamic reversibility.