Non-equilibrium thermodynamics of stochastic systems with odd and even variables

TL;DR

This paper develops a thermodynamic framework for stochastic systems with odd and even variables, deriving fluctuation theorems and clarifying the roles of different entropy production components.

Contribution

It introduces a new formalism for entropy production in systems with directional variables, extending previous models to non-equilibrium stochastic dynamics.

Findings

Derived an integral fluctuation theorem for generalised house-keeping heat.

Separated total entropy production into excess, transient, and generalised house-keeping heat.

Extended formalism to systems with asymmetric stationary distributions for odd variables.

Abstract

The total entropy production of stochastic systems can be divided into three quantities. The first corresponds to the excess heat, whilst the second two comprise the house-keeping heat. We denote these two components the transient and generalised house-keeping heat and we obtain an integral fluctuation theorem for the latter, valid for all Markovian stochastic dynamics. A previously reported formalism is obtained when the stationary probability distribution is symmetric for all variables that are odd under time reversal which restricts consideration of directional variables such as velocity.