Illustration of the Jarzynski nonequilibrium work relation for an ideal gas

TL;DR

This paper demonstrates the Jarzynski nonequilibrium work relation using a classical ideal gas model with a moving piston, verifying the relation through theoretical analysis and discussing its practical implications.

Contribution

It provides a clear illustration and verification of the Jarzynski relation in a simple ideal gas system, highlighting its practical applicability.

Findings

Verification of the Jarzynski relation for an ideal gas

Analysis of work distributions in forward and reverse processes

Discussion on practical realization of the relation

Abstract

The Jarzynski relation is a recently discovered result relating the average exponential of the work done under nonequilibrium conditions to an equilibrium free energy difference. We illustrate this remarkable relation by considering the expansion and compression of a classical ideal gas particle inside a cavity with a moving piston in one dimension. Using a simple relationship between the distributions of the nonequilibrium work done in the two (forward and reverse) processes, we verify the Jarzynski relation and discuss the practical realization of the Jarzynski equality for the model.