Comparison of far-from-equilibrium work relations

TL;DR

This paper compares recent and historical work relations in nonequilibrium thermodynamics, clarifying their differences, physical interpretations, and illustrating the concepts with a simple model.

Contribution

It elucidates the relationship between modern fluctuation theorems and earlier work relations, providing clarity on definitions of work in nonequilibrium systems.

Findings

Demonstrates the connection between different work relations

Clarifies physical interpretation of work definitions

Provides an undergraduate-level example model

Abstract

Recent theoretical predictions and experimental measurements have demonstrated that equilibrium free energy differences can be obtained from exponential averages of nonequilibrium work values. These results are similar in structure, but not equivalent, to predictions derived nearly three decades ago by Bochkov and Kuzovlev, which are also formulated in terms of exponential averages but do not involve free energy differences. In the present paper the relationship between these two sets of results is elucidated, then illustrated with an undergraduate-level solvable model. The analysis also serves to clarify the physical interpretation of different definitions of work that have been used in the context of thermodynamic systems driven away from equilibrium.