Entropy of the quantum work distribution

TL;DR

This paper explores the entropy of quantum work distributions, revealing bounds related to initial entropy and quantum coherence, and demonstrates its effectiveness in detecting localization transitions in quantum systems.

Contribution

It introduces a new entropy-based framework for analyzing quantum work distributions, linking them to initial entropy and quantum coherence, and applies it to the Aubry-André-Harper model.

Findings

Entropy bounds depend on initial diagonal entropy and quantum coherence.

Work distribution entropy signals localization transition clearly.

Moments of the distribution are less informative than entropy.

Abstract

The statistics of work done on a quantum system can be quantified by the two-point measurement scheme. We show how the Shannon entropy of the work distribution admits a general upper bound depending on the initial diagonal entropy, and a purely quantum term associated to the relative entropy of coherence. We demonstrate that this approach captures strong signatures of the underlying physics in a diverse range of settings. In particular, we carry out a detailed study of the Aubry-Andr\'e-Harper model and show that the entropy of the work distribution conveys very clearly the physics of the localization transition, which is not apparent from the statistical moments.