Colloquium. Quantum Fluctuation Relations: Foundations and Applications

TL;DR

This paper provides a comprehensive, self-contained overview of quantum fluctuation relations, emphasizing their theoretical foundations, historical context, and recent experimental applications in quantum thermodynamics and transport.

Contribution

It offers a unified exposition of quantum fluctuation relations, clarifies unresolved fundamental issues, and connects these relations to nonlinear response theory and experimental quantum thermodynamics.

Findings

Quantum fluctuation relations are exact and foundational for nonequilibrium thermodynamics.

The paper clarifies fundamental issues in quantum fluctuation relations.

Recent experimental applications demonstrate the practical relevance of these relations.

Abstract

Two fundamental ingredients play a decisive role in the foundation of fluctuation relations: the principle of microreversibility and the fact that thermal equilibrium is described by the Gibbs canonical ensemble. Building on these two pillars we guide the reader through a self-contained exposition of the theory and applications of quantum fluctuation relations. These are exact results that constitute the fulcrum of the recent development of nonequilibrium thermodynamics beyond the linear response regime. The material is organized in a way that emphasizes the historical connection between quantum fluctuation relations and (non)-linear response theory. We also attempt to clarify a number of fundamental issues which were not completely settled in the prior literature. The main focus is on (i) work fluctuation relations for transiently driven closed or open quantum systems, and (ii) on fluctuation relations for heat and matter exchange in quantum transport settings. Recently performed and proposed experimental applications are presented and discussed.