Fluctuation theorems from Bayesian retrodiction

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.

arXiv commentv4: 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

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Cited by in corpus (33)

• From time-reversal symmetry to quantum Bayes' rules
• Reversing Lindblad Dynamics via Continuous Petz Recovery Map
• Axioms for retrodiction: achieving time-reversal symmetry with a prior
• Thermodynamics of computations with absolute irreversibility, unidirectional transitions, and stochastic computation times
• Characterizing (non-)Markovianity through Fisher Information
• State retrieval beyond Bayes' retrodiction
• Observational entropy, coarse quantum states, and Petz recovery: information-theoretic properties and bounds
• Maxwell's Demon walks into Wall Street: Stochastic Thermodynamics meets Expected Utility Theory
• Dependence of integrated, instantaneous, and fluctuating entropy production on the initial state in quantum and classical processes
• The Near-optimal Performance of Quantum Error Correction Codes
• Unruh phenomena and thermalization for qudit detectors
• Jarzynski-like Equality of Nonequilibrium Information Production Based on Quantum Cross Entropy
• Conditional entropy production and quantum fluctuation theorem of dissipative information: Theory and experiments
• Witnessing quantum chaos using observational entropy
• Quantum Bayesian Inference in Quasiprobability Representations
• On the generic increase of observational entropy in isolated systems
• Universal validity of the second law of information thermodynamics
• Quantum Bayes' rule and Petz transpose map from the minimum change principle
• Symmetry-induced fluctuation relations in open quantum systems
• Von Neumann's information engine without the spectral theorem
• Role of Dilations in Reversing Physical Processes: Tabletop Reversibility and Generalized Thermal Operations
• Observational entropy with general quantum priors
• Quasiprobability fluctuation theorem behind the spread of quantum information
• Petz recovery maps for qudit quantum channels
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• Jarzyski's equality and Crooks' fluctuation theorem for general Markov chains with application to decision-making systems
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• A Retrodictive Approach to Quantum State Smoothing
• Fluctuation Theorems with Retrodiction rather than Reverse Processes
• Bipartite quantum states admitting a causal explanation
• Quantifying Irreversibility via Bayesian Subjectivity for Classical & Quantum Linear Maps