Fluctuation theorems from Bayesian retrodiction

TL;DR

This paper demonstrates that the concept of a reverse process in statistical mechanics and quantum systems naturally emerges from Bayesian retrodiction, unifying and generalizing fluctuation theorems.

Contribution

It introduces a Bayesian retrodictive framework for deriving reverse processes, extending fluctuation theorems to broader contexts in classical and quantum systems.

Findings

Reverse channels arise naturally from Bayesian retrodiction.

Classical and quantum fluctuation theorems are consistent with retrodictive arguments.

Generalized fluctuation relations encompass previous results and new corrections.

Abstract

Quantitative studies of irreversibility in statistical mechanics often involve the consideration of a reverse process, whose definition has been the object of many discussions, in particular for quantum mechanical systems. Here we show that the reverse channel very naturally arises from Bayesian retrodiction, both in classical and quantum theories. Previous paradigmatic results, such as Jarzynski's equality, Crooks' fluctuation theorem, and Tasaki's two-measurement fluctuation theorem for closed driven quantum systems, are all shown to be consistent with retrodictive arguments. Also, various corrections that were introduced to deal with nonequilibrium steady states or open quantum systems are justified on general grounds as remnants of Bayesian retrodiction. More generally, with the reverse process constructed on consistent logical inference, fluctuation relations acquire a much broader form and scope.