A possible generalized form of Jarzynski equality

TL;DR

This paper proposes a generalized form of the Jarzynski equality that applies to systems where the standard condition does not hold, supported by theoretical experiments and simulations, with potential nanoscale experimental verification.

Contribution

It introduces a broader version of the Jarzynski equality applicable to systems violating the traditional phase space contraction condition.

Findings

A generalized Jarzynski equality is theoretically verified.

Numerical simulations support the existence of the generalized form.

Potential for experimental confirmation at the nanoscale.

Abstract

The crucial condition in the derivation of the Jarzynski equality (JE) from the fluctuation theorem is that the time integral of the phase space contraction factor can be exactly expressed as the entropy production resulting from the heat absorbed by the system from the thermal bath. For the system violating this condition, a more general form of JE may exist. This existence is verified by three \textit{Gedanken} experiments and numerical simulations, and may be confirmed by the real experiment in the nanoscale.