Thermodynamic transformations of nonequilibrium states

TL;DR

This paper develops a framework for defining and analyzing a renormalized work in nonequilibrium thermodynamics, showing it satisfies a Clausius inequality and relates to fluctuation theory, thus extending classical thermodynamics to nonequilibrium states.

Contribution

It introduces a natural definition of renormalized work for time-dependent nonequilibrium processes and links it to the quasi potential without relying on rare fluctuation analysis.

Findings

Renormalized work satisfies a Clausius inequality.

Quasi static transformations minimize the renormalized work.

The quasi potential is characterized without involving rare fluctuations.

Abstract

We consider a macroscopic system in contact with boundary reservoirs and/or under the action of an external field. We discuss the case in which the external forcing depends explicitly on time and drives the system from a nonequilibrium state to another one. In this case the amount of energy dissipated along the transformation becomes infinite when an unbounded time window is considered. 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. We then discuss its thermodynamic relevance by showing that it satisfies a Clausius inequality and that quasi static transformations minimize the renormalized work. In addition, we connect the renormalized work to the quasi potential describing the fluctuations in the stationary nonequilibrium ensemble. The latter result provides a characterization of the quasi potential that does not involve rare fluctuations.