The exchange fluctuation theorem in quantum mechanics

TL;DR

This paper investigates the validity of the exchange fluctuation theorem in quantum heat transfer, revealing it generally fails with finite coupling unless a specific commutable-coupling condition is met, supported by explicit model calculations.

Contribution

It identifies a necessary condition for the exchange fluctuation theorem to hold with finite heat transfer in quantum systems, expanding understanding beyond weak coupling scenarios.

Findings

Deviation from the theorem vanishes as coupling weakens

The commutable-coupling condition ensures the theorem holds exactly

Explicit models confirm the theoretical predictions

Abstract

We study the heat transfer between two finite quantum systems initially at different temperatures. We find that a recently proposed fluctuation theorem for heat exchange, namely the exchange fluctuation theorem [C. Jarzynski and D. K. Wojcik, Phys. Rev. Lett. 92, 230602 (2004)], does not generally hold in the presence of a finite heat transfer as in the original form proved for weak coupling. As the coupling is weakened, the deviation from the theorem and the heat transfer vanish in the same order of the coupling. We then discover a condition for the exchange fluctuation theorem to hold in the presence of a finite heat transfer, namely the commutable-coupling condition. We explicitly calculate the deviation from the exchange fluctuation theorem as well as the heat transfer for simple models. We confirm for the models that the deviation indeed has a finite value as far as the coupling between the two systems is finite except for the special point of the commutable-coupling condition. We also confirm analytically that the commutable-coupling condition indeed lets the exchange fluctuation theorem hold exactly under a finite heat transfer.