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Nonequilibrium work-Hamiltonian connection for a microstate plays a centralrole in diverse branches of statistical thermodynamics (fluctuation theorems,quantum thermodynamics, stochastic thermodynamics, etc.). We show that thechange in the Hamiltonian for a microstate should be identified with the workdone by it, and not the work done on it. This contradicts the current practicein the field. The difference represents a contribution whose average gives thework that is dissipated due to irreversibility. As the latter has beenoverlooked, the current identification does not properly account forirreversibilty. As an example, we show that the corrected version ofJarzynski's relation can be applied to free expansion, where the originalrelation fails. Thus, the correction has far-reaching consequences and requiresreassessment of current applications.

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