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

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.