The distribution function of entropy flow in stochastic systems

TL;DR

This paper derives a differential equation for the entropy flow distribution in stochastic systems, introduces an effective trajectory-sampling algorithm, and validates it with experimental and simulation results.

Contribution

It provides a simple derivation of the entropy flow distribution equation and introduces a new sampling algorithm applicable to complex stochastic systems.

Findings

The derived differential equation matches experimental data.

The sampling algorithm is effective at finite times.

Successful application to asymmetric simple exclusion process.

Abstract

We obtain a simple direct derivation of the differential equation governing the entropy flow probability distribution function of a stochastic system first obtained by Lebowitz and Spohn. Its solution agrees well with the experimental results of Tietz et al [2006 {\it Phys. Rev. Lett.} {\bf 97} 050602]. A trajectory-sampling algorithm allowing to evaluate the entropy flow distribution function is introduced and discussed. This algorithm turns out to be effective at finite times and in the case of time-dependent transition rates, and is successfully applied to an asymmetric simple exclusion process.