Note on the Jarzynski Equality

TL;DR

This paper critiques the derivation of the Jarzynski Equality, arguing it is flawed, and questions its experimental validation, but suggests it might still be useful as an approximation in certain molecular measurements.

Contribution

The paper identifies a flaw in the derivation of the Jarzynski Equality and questions the validity of its experimental confirmation, proposing it as a potential approximation.

Findings

The derivation of the Jarzynski Equality is flawed due to unjustified weighting.

Experimental results by Liphardt et al. do not confirm the equality.

The equality may serve as a useful approximation in molecular measurements.

Abstract

The Jarzynski Equality relates the free energy difference between two equilibrium states of a system to the average of the work over all irreversible paths to go from one state to the other. We claim that the derivation of this equality is flawed, introducing an ad hoc and unjustified weighting factor which handles improperly the heat exchange with a heat bath. Therefore Liphardt et al's experiment cannot be viewed as a confirmation of this equality, although the numerical deviations between the two are small. However, the Jarzynski Equality may well be a useful approximation, e.g. in measurements on single molecules in solution.