2020/09/30 by Francesco Buscemi, Valerio Scarani
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Artificial intelligence #Bayesian inference #Bayesian probability #Computer science #Inference #Mathematical economics #Mathematics #Non-equilibrium thermodynamics #Physics #Process (computing) #Quantum #Quantum Mechanics and Applications #Quantum mechanics #Scope (computer science) #Statistical Mechanics and Entropy #Statistical physics #Theoretical physics #cond-mat.stat-mech #quant-ph
paper · pdf · doi:10.1103/physreve.103.052111
published as Phys. Rev. E 103, 052111 (2021) · v4: greatly expanded and with new examples, accepted for publication on PRE; v3: various improvements in the presentation and examples added (fluctuation relations for f-divergences); v2: discussion expanded, refs added, now a little more than 5 two-column pages; v1:5 two-column pages
arxiv created 2021/04/08 · openalex publication_date 2021/05/06 · arxiv updated 2021/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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, in both 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.