Entropy of the quantum work distribution

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