A nonequilibrium extension of the Clausius heat theorem

TL;DR

This paper extends the Clausius heat theorem to nonequilibrium diffusions with nonconservative forces using a novel heat decomposition based on the Minimum Entropy Production Principle, applicable far from equilibrium.

Contribution

It introduces a nonequilibrium extension of the Clausius theorem that does not rely on near-equilibrium assumptions, applicable to complex diffusive systems.

Findings

The extended heat theorem holds for arbitrary driving forces.

The decomposition scheme is based on an exact variant of the Minimum Entropy Production Principle.

The relation between Shannon entropy change and time-reversal antisymmetry is established.

Abstract

We generalize the Clausius (in)equality to overdamped mesoscopic and macroscopic diffusions in the presence of nonconservative forces. In contrast to previous frameworks, we use a decomposition scheme for heat which is based on an exact variant of the Minimum Entropy Production Principle as obtained from dynamical fluctuation theory. This new extended heat theorem holds true for arbitrary driving and does not require assumptions of local or close to equilibrium. The argument remains exactly intact for diffusing fields where the fields correspond to macroscopic profiles of interacting particles under hydrodynamic fluctuations. We also show that the change of Shannon entropy is related to the antisymmetric part under a modified time-reversal of the time-integrated entropy flux.