A Quantum Fluctuation Theorem

TL;DR

This paper establishes a quantum fluctuation theorem relating the probabilities of energy changes in periodically driven quantum systems, applicable to both thermostated and isolated cases, revealing a fundamental symmetry in energy transfer statistics.

Contribution

It introduces a model-independent, parameter-free fluctuation theorem for quantum systems under periodic driving, extending classical fluctuation relations to the quantum domain.

Findings

Proves the relation P(e)/P(-e)=e^{eta e} for quantum systems.

Applies to both thermostated and isolated quantum systems.

Provides a fundamental symmetry in quantum energy transfer statistics.

Abstract

We consider a quantum system strongly driven by forces that are periodic in time. The theorem concerns the probability $P(e)$ of observing a given energy change $e$ after a number of cycles. If the system is thermostated by a (quantum) thermal bath, $e$ is the total amount of energy transferred to the bath, while for an isolated system $e$ is the increase in energy of the system itself. Then, we show that $P(e)/P(-e)=e^{\beta e}$, a parameter-free, model-independent relation.