A simple proof of the Jarzynski equality?

TL;DR

This paper presents a straightforward derivation of the Jarzynski equality, which relates work done during non-equilibrium processes to free energy differences, explaining its experimental success even in irreversible cases.

Contribution

It provides a simple proof of the Jarzynski equality, clarifying its validity for both reversible and irreversible transformations and shedding light on recent experimental findings.

Findings

The derivation is simple and general.

The equality holds regardless of the transformation reversibility.

Experimental tests of the equality are successful even in irreversible cases.

Abstract

In this short communication, I give a very simple derivation of the Jarzynski equality, which allows to compute the free energy difference of a body, which is driven between two equilibrium states $A$ and $B$ by an external (time-dependent) force, from the probability distribution function of the work done on the system, regardless of the nature of the transformation (reversible or irreversible) between the states $A$ and $B$. It perhaps throws some light on the debate recently started by Cohen and coworkers, and perhaps explains why all the experiments which has been performed in order to test the Jarzynski equality are successful, even in very defavorable (irreversible) cases (and more strikingly, when the state $B$ is not an equilibrium one).