Entropy production along a stochastic trajectory and an integral fluctuation theorem

TL;DR

This paper investigates entropy production in stochastic non-equilibrium systems, demonstrating that the sum of particle and medium entropy production obeys a fluctuation theorem regardless of initial conditions or driving protocols.

Contribution

It derives a fluctuation theorem for the total entropy production along a stochastic trajectory, applicable to various non-equilibrium dynamics.

Findings

The sum of particle and medium entropy production satisfies a fluctuation theorem.

The fluctuation theorem holds for arbitrary initial conditions and time-dependent driving.

The results unify entropy production concepts in stochastic thermodynamics.

Abstract

For stochastic non-equilibrium dynamics like a Langevin equation for a colloidal particle or a master equation for discrete states, entropy production along a single trajectory is studied. It involves both genuine particle entropy and entropy production in the surrounding medium. The integrated sum of both $\Delta s\t$is shown to obey a fluctuation theorem $<\exp[-\Delta s\t]> =1$ for arbitrary initial conditions and arbitrary time-dependent driving over a finite time interval.