Entropy production in systems with random transition rates

TL;DR

This paper analyzes the entropy production in finite-state systems with random transition rates, deriving exact distributions for contributions near equilibrium, revealing connections to Joule's law and Gaussian fluctuations.

Contribution

It provides an exact calculation of the distribution of entropy production contributions in systems with random transition rates near equilibrium.

Findings

Entropy production has two main contributions with distinct distributions.

One contribution relates to Joule's law, representing heat dissipation.

The other contribution follows a Gaussian distribution with extensive mean and finite variance.

Abstract

We study the entropy production of a system with a finite number of states connected by random transition rates. The stationary entropy production, driven out of equilibrium both by asymmetric transition rates and by an external probability current, is shown to be composed of two contributions whose exact distributions are calculated in the large system size and close to equilibrium. The first contribution is related to Joule's law for the heat dissipated in a classical electrical circuit whereas the second one has a Gaussian distribution with an extensive average and a finite variance.