Clausius inequality and optimality of quasi static transformations for nonequilibrium stationary states

TL;DR

This paper introduces a renormalized work concept for nonequilibrium stationary states, demonstrating it satisfies a Clausius inequality and is minimized in quasi-static transformations, linking it to macroscopic fluctuation theory.

Contribution

It defines a renormalized work for nonequilibrium states and proves it obeys a Clausius inequality, with equality in the quasi-static limit, connecting to the quasi potential.

Findings

Renormalized work satisfies a Clausius inequality.

Equality holds for very slow, quasi-static transformations.

Links renormalized work to the macroscopic fluctuation theory quasi potential.

Abstract

Nonequilibrium stationary states of thermodynamic systems dissipate a positive amount of energy per unit of time. If we consider transformations of such states that are realized by letting the driving depend on time, the amount of energy dissipated in an unbounded time window becomes then infinite. Following the general proposal by Oono and Paniconi and using results of the macroscopic fluctuation theory, we give a natural definition of a renormalized work performed along any given transformation. We then show that the renormalized work satisfies a Clausius inequality and prove that equality is achieved for very slow transformations, that is in the quasi static limit. We finally connect the renormalized work to the quasi potential of the macroscopic fluctuation theory, that gives the probability of fluctuations in the stationary nonequilibrium ensemble.