Nonequilibrium Work and its Hamiltonian Connection for a Microstate in Nonequilibrium Statistical Thermodynamics: A Case of Mistaken Identity

TL;DR

This paper clarifies the proper identification of nonequilibrium work with Hamiltonian changes for microstates, revealing a correction to established relations like Jarzynski's and emphasizing the importance of accounting for irreversibility.

Contribution

It demonstrates that the change in Hamiltonian should be identified with work done by the microstate, not on it, leading to a corrected form of fluctuation relations.

Findings

The change in Hamiltonian equals work done by the microstate.

The correction improves the applicability of Jarzynski's relation to free expansion.

Current practice overlooks irreversibility contributions.

Abstract

Nonequilibrium work-Hamiltonian connection for a microstate plays a central role in diverse branches of statistical thermodynamics (fluctuation theorems, quantum thermodynamics, stochastic thermodynamics, etc.). We show that the change in the Hamiltonian for a microstate should be identified with the work done by it, and not the work done on it. This contradicts the current practice in the field. The difference represents a contribution whose average gives the work that is dissipated due to irreversibility. As the latter has been overlooked, the current identification does not properly account for irreversibilty. As an example, we show that the corrected version of Jarzynski's relation can be applied to free expansion, where the original relation fails. Thus, the correction has far-reaching consequences and requires reassessment of current applications.