Fluctuation Relation for Heat

TL;DR

This paper derives a modified fluctuation relation for heat in nonequilibrium systems, accounting for correlations between heat and energy change, and verifies it in a linear diffusion model.

Contribution

It introduces a new fluctuation relation for heat that incorporates correlations with energy change, extending previous work on work fluctuation theorems.

Findings

Derived the fluctuation relation for heat in Langevin systems.

Confirmed the relation through analysis of a linear diffusion system.

Showed the correlation affects fluctuation behavior even at long times.

Abstract

We present a fluctuation relation for heat dissipation in a nonequilibrium system. A nonequilibrium work is known to obey the fluctuation theorem in any time interval $t$. A heat, which differs from a work by an energy change, is shown to satisfy a modified fluctuation relation. Modification is brought by correlation between a heat and an energy change during nonequilibrium processes whose effect may not be negligible even in the $t\to\infty$ limit. The fluctuation relation is derived for overdamped Langevin equation systems, and tested in a linear diffusion system.