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