Hierarchical structure of fluctuation theorems for a driven system in contact with multiple heat reservoirs

TL;DR

This paper uncovers a hierarchical structure of fluctuation theorems for driven systems with multiple heat reservoirs, showing that only joint distributions of work and heat satisfy these theorems, and provides a method to compute their statistics.

Contribution

It introduces a unified framework for fluctuation theorems involving work and heat in multi-reservoir systems using a step-by-step coarse-graining approach.

Findings

Joint distribution of work and heat satisfies fluctuation theorems.

Hierarchical structure of fluctuation theorems is derived.

Verification with classical Brownian particle confirms theoretical results.

Abstract

For driven open systems in contact with multiple heat reservoirs, we find the marginal distributions of work or heat do not satisfy any fluctuation theorem, but only the joint distribution of work and heat satisfies a family of fluctuation theorems. A hierarchical structure of these fluctuation theorems is discovered from microreversibility of the dynamics by adopting a step-by-step coarse-graining procedure in both classical and quantum regimes. Thus, we put all fluctuation theorems concerning work and heat into a unified framework. We also propose a general method to calculate the joint statistics of work and heat in the situation of multiple heat reservoirs via the Feynman-Kac equation. For a classical Brownian particle in contact with multiple heat reservoirs, we verify the validity of the fluctuation theorems for the joint distribution of work and heat.