Entropy production in full phase space for continuous stochastic dynamics

TL;DR

This paper analyzes the total entropy production in continuous stochastic systems with full phase space dynamics, identifying fluctuation theorems and exploring their properties through specific physical examples.

Contribution

It provides a detailed decomposition of entropy production components in Markovian stochastic dynamics with multiplicative noise, highlighting their fluctuation properties and physical interpretations.

Findings

Two entropy components obey fluctuation theorems and are positive on average.

The third component does not obey fluctuation theorems and is not solely linked to irreversibility.

Application to heat conduction and drift-diffusion demonstrates the theoretical framework.

Abstract

The total entropy production and its three constituent components are described both as fluctuating trajectory-dependent quantities and as averaged contributions in the context of the continuous Markovian dynamics, described by stochastic differential equations with multiplicative noise, of systems with both odd and even coordinates with respect to time reversal, such as dynamics in full phase space. Two of these constituent quantities obey integral fluctuation theorems and are thus rigorously positive in the mean by Jensen's inequality. The third, however, is not and furthermore cannot be uniquely associated with irreversibility arising from relaxation, nor with the breakage of detailed balance brought about by non-equilibrium constraints. The properties of the various contributions to total entropy production are explored through the consideration of two examples: steady state heat conduction due to a temperature gradient, and transitions between stationary states of drift-diffusion on a ring, both in the context of the full phase space dynamics of a single Brownian particle.