Entropy production in nonequilibrium thermodynamics: a review

TL;DR

This review discusses the conceptual and technical challenges of defining entropy production in nonequilibrium stationary systems, questioning the existence of a state function analogous to entropy.

Contribution

It reviews recent philosophical and technical approaches to defining entropy in nonequilibrium systems, highlighting unresolved issues and new insights into phase space contraction.

Findings

Entropy may not be a well-defined state function in nonequilibrium stationary systems.

Technical attempts to define entropy reveal unsatisfactory aspects, suggesting nonexistence of a true entropy function.

New properties of phase space contraction are identified in the context of nonequilibrium thermodynamics.

Abstract

Entropy might be a not well defined concept if the system can undergo transformations involving stationary nonequilibria. It might be analogous to the heat content (once called ``caloric'') in transformations that are not isochoric (i.e. which involve mechanical work): it could be just a quantity that can be transferred or created, like heat in equilibrium. The text first reviews the philosophy behind a recently proposed definition of entropy production in nonequilibrium stationary systems. A detailed technical attempt at defining the entropy of a stationary states via their variational properties follows: the unsatisfactory aspects of the results add arguments in favor of the nonexistence of a function of state to be identified with entropy; at the same time new aspects and properties of the phase space contraction emerge.