Entropy of stationary nonequilibrium measures of boundary driven symmetric simple exclusion processes

TL;DR

This paper investigates the entropy characteristics of stationary nonequilibrium states in boundary-driven symmetric simple exclusion processes, highlighting differences from local equilibrium states and Gibbs-Shannon entropy.

Contribution

It provides a detailed analysis of the entropy of nonequilibrium stationary measures, contrasting them with local equilibrium and Gibbs-Shannon entropies.

Findings

Entropy of nonequilibrium states differs from local equilibrium states.

The entropy of stationary nonequilibrium measures is explicitly characterized.

Differences from Gibbs-Shannon entropy are elucidated.

Abstract

We examine the entropy of stationary nonequilibrium measures of boundary driven symmetric simple exclusion processes. In contrast with the Gibbs--Shannon entropy \cite{B, DLS2}, the entropy of nonequilibrium stationary states differs from the entropy of local equilibrium states.