Correcting the Mistaken Identification of Nonequilibrium Microscopic Work

TL;DR

This paper corrects a fundamental mistake in defining microscopic work, showing the importance of internal energy changes and deriving a new work relation that applies even in cases where the Jarzynski equality fails.

Contribution

It introduces a corrected definition of microscopic work accounting for internal energy changes and proposes a new work relation valid for free expansion and other processes.

Findings

Corrected the identification of microscopic work as dE_k = -dW_k.

Showed that internal energy changes contribute to dissipation even in reversible processes.

Derived a new work relation that remains valid where the Jarzynski equality does not.

Abstract

The energy change dE_k for the kth microstate is erroneously equated with the external work done on the microstate. It ignores the ubiquitous internal energy change d_iW_k due to force imbalance between the internal and external forces. We show that this contribution is present even in a reversible process, which is a surprise. We show that the correct identification is dE_k=-dW_k, where dW_k is the generalized work done by the microstate. We prove that the thermodynamic average of the internal work gives dissipation and is not captured by the external work. The latter effectively sets d_iW_k =0 and results in no dissipation. Using dW_k to account for irreversibility, we obtain a new work relation that works even for free expansion, where the Jarzynski equality fails. In the new work relation, dW_k depends only on the energies of the initial and final states and not on the actual process. This makes the new relation very different from the Jarzynski equality. The correction has far-reaching consequences and requires reassessment of current applications of external work in theoretical physics.