Fluctuation theorems for autonomous work in the quantum regime

Research Overview

This paper extends the framework of fluctuation theorems—universal constraints on nonequilibrium work—from classical autonomous systems to the quantum regime. In nonautonomous systems, work is typically defined via an externally prescribed protocol. In contrast, autonomous systems treat the work source as a dynamical variable that is coupled to the system of interest, meaning the system exerts a backaction on the work source. While this has been well-studied in classical stochastic thermodynamics, the quantum version is complicated by the uncertainty principle and the non-classical nature of quantum trajectories.

The authors propose a framework based on successive projective measurements of an observable of the work source and the Hamiltonian of the system. By measuring these at both the initial and final times, they define inclusive work for autonomous quantum systems. They utilize unitary reversibility and the assumption of initial thermal equilibrium to derive Jarzynski-type and Crooks-type equalities. These relations incorporate an entropy-like term that accounts for the change in the work source's measurement statistics, effectively capturing the backaction that is absent in nonautonomous models.

Findings and Implications

The study demonstrates these theorems using the Dicke model, where a single-mode radiation field (the system) interacts with an ensemble of two-level atoms (the work source). The results show that the fluctuation theorems hold even when the backaction is significant. A critical finding is that, due to quantum noncommutativity, these autonomous relations do not consistently reduce to nonautonomous ones, even when the work source is large and backaction is negligible. This highlights a fundamental quantum obstruction: the observable of the work source cannot evolve deterministically as a classical control parameter, as its distribution inevitably broadens.