Quantum work statistics at strong reservoir coupling

TL;DR

This paper introduces a polaron transformation method to compute quantum work statistics at strong reservoir coupling, preserving fluctuation theorems and revealing environmental effects in driven quantum systems.

Contribution

It presents a novel approach using a polaron transformation to analyze quantum work at strong coupling, extending stochastic thermodynamics beyond weak-coupling regimes.

Findings

Work distribution invariance under the transformation

Reproduction of Jarzynski fluctuation theorem

Signatures of environment coupling in Landau-Zener transitions

Abstract

Calculating the stochastic work done on a quantum system while strongly coupled to a reservoir is a formidable task, requiring the calculation of the full eigenspectrum of the combined system and reservoir. Here we show that this issue can be circumvented by using a polaron transformation that maps the system into a new frame where weak-coupling theory can be applied. It is shown that the work probability distribution is invariant under this transformation, allowing one to compute the full counting statistics of work at strong reservoir coupling. Crucially this polaron approach reproduces the Jarzynski fluctuation theorem, thus ensuring consistency with the laws of stochastic thermodynamics. We apply our formalism to a system driven across the Landau-Zener transition, where we identify clear signatures in the work distribution arising from a non-negligible coupling to the environment. Our results provide a new method for studying the stochastic thermodynamics of driven quantum systems beyond Markovian, weak-coupling regimes.