Microscopic analysis of Clausius-Duhem processes

TL;DR

This paper introduces a microscopic quantity that relates the entropy difference between equilibrium states to irreversible processes, providing new statistical insights into the Clausius-Duhem inequality and extending to nonequilibrium initial and final states.

Contribution

It constructs a microscopic quantity whose average depends only on the end states, enabling new statistical formulations of thermodynamic inequalities and their generalizations.

Findings

Provides a microscopic basis for entropy differences in thermodynamics.

Derives two statistical statements of the Clausius-Duhem inequality.

Extends the framework to nonequilibrium initial and final states.

Abstract

Given a thermodynamic process which carries a system from one equilibrium state to another, we construct a quantity whose average, over an ensemble of microscopic realizations of the process, depends only on these end states, even if at intermediate times the system is out of equilibrium. This result: (1) can be used to express the entropy difference between two equilibrium states in terms of an irreversible process connecting them, (2) leads to two statistical statements of the Clausius-Duhem inequality, and (3) can be generalized to situations in which the system begins and/or ends in nonequilibrium states.