Gibbs entropy and irreversible thermodynamics

TL;DR

This paper critically examines the use of Gibbs entropy in connecting microscopic dynamics to macroscopic nonequilibrium thermodynamics, highlighting difficulties and limitations in current approaches.

Contribution

The authors analyze existing models linking dynamical systems to Irreversible Thermodynamics, identifying key challenges and questioning the suitability of Gibbs entropy in this context.

Findings

Gibbs entropy may not adequately characterize nonequilibrium states.

Simplified models show potential but face significant difficulties.

Establishing a physically relevant connection remains challenging.

Abstract

Recently a number of approaches has been developed to connect the microscopic dynamics of particle systems to the macroscopic properties of systems in nonequilibrium stationary states, via the theory of dynamical systems. This way a direct connection between dynamics and Irreversible Thermodynamics has been claimed to have been found. However, the main quantity used in these studies is a (coarse-grained) Gibbs entropy, which to us does not seem suitable, in its present form, to characterize nonequilibrium states. Various simplified models have also been devised to give explicit examples of how the coarse-grained approach may succeed in giving a full description of the Irreversible Thermodynamics. We analyze some of these models pointing out a number of difficulties which, in our opinion, need to be overcome in order to establish a physically relevant connection between these models and Irreversible Thermodynamics.