Fluctuation theorems in driven open quantum systems

TL;DR

This paper derives fluctuation theorems for driven open quantum systems, connecting work, heat, and energy changes, and demonstrates their validity under weak coupling and initial equilibrium conditions.

Contribution

It introduces a characteristic function framework for joint measurements of energy changes and proves fluctuation theorems like Tasaki-Crooks and Jarzynski in quantum settings.

Findings

Work satisfies Tasaki-Crooks theorem.

Work satisfies Jarzynski equality.

Framework applies to weakly coupled systems in equilibrium.

Abstract

The characteristic function for the joint measurement of the changes of two commuting observables upon an external forcing of a quantum system is derived. In particular, the statistics of the internal energy, the exchanged heat and the work of a quantum system that {\it weakly} couples to its environment is determined in terms of the energy changes of the system and the environment due to the action of a classical, external force on the system. If the system and environment initially are in a canonical equilibrium, the work performed on the system is shown to satisfy the Tasaki-Crooks theorem and the Jarzynski equality.