Integral fluctuation theorem for the housekeeping heat

TL;DR

This paper proves an integral fluctuation theorem for the housekeeping heat in nonequilibrium steady states, revealing fundamental properties of dissipated heat and its statistical behavior.

Contribution

It introduces a new integral fluctuation theorem for the housekeeping heat, extending the understanding of thermodynamic fluctuations in nonequilibrium systems.

Findings

Proves the integral fluctuation theorem $ ext{E}[e^{-eta Q_{hk}}]=1$ for arbitrary driven steady states.

Analyzes Gaussian limiting cases of the theorem.

Discusses differences from Hatano-Sasa and Jarzynski relations.

Abstract

The housekeeping heat $Q\hk$ is the dissipated heat necessary to maintain the violation of detailed balance in nonequilibrium steady states. By analyzing the evolution of its probability distribution, we prove an integral fluctuation theorem $\mean{\exp[-\beta Q\hk]}=1$ valid for arbitrary driven transitions between steady states. We discuss Gaussian limiting cases and the difference between the new theorem and both the Hatano-Sasa and the Jarzynski relation.