Entropy of non-equilibrium stationary measures of boundary driven TASEP

TL;DR

This paper analyzes the entropy behavior of non-equilibrium stationary states in boundary-driven TASEP, showing convergence to local equilibrium entropy and Gaussian fluctuations with specific exceptions.

Contribution

It demonstrates the convergence of the Gibbs-Shannon entropy to local equilibrium entropy and characterizes the fluctuations, including exceptions in the maximal phase regime.

Findings

Gibbs-Shannon entropy converges to local equilibrium entropy.

Fluctuations are Gaussian except in the maximal phase regime.

Identifies conditions where fluctuations deviate from Gaussian behavior.

Abstract

We examine the entropy of non-equilibrium stationary states of boundary driven totally asymmetric simple exclusion processes. As a consequence, we obtain that the Gibbs-Shannon entropy of the non equilibrium stationary state converges to the Gibbs-Shannon entropy of the local equilibrium state. Moreover, we prove that its fluctuations are Gaussian, except when the mean displacement of particles produced by the bulk dynamics agrees with the particle flux induced by the density reservoirs in the maximal phase regime.