Irreversibility is usually captured by a comparison between the process that happens and a corresponding “reverse process”. In the last decades, this comparison has been extensively studied through fluctuation relations which are often understood as generalizations of the thermodynamic second law. Here [1,2], we revisit fluctuation relations (both classical [3-5] and quantum [6,7]) from a more information-theoretic standpoint, suggested decades ago by Watanabe [8], that the comparison should involve the prediction and the retrodiction on the unique process, rather than two physical processes. For quantum fluctuation theorems, in particular, Petz Recovery Map [9-12] plays a central role in retrodictive inference.

Through this we identify a necessary and sufficient condition for a retrodictive reading of fluctuation relations. The retrodictive narrative also brings to the fore the possibility of deriving fluctuation relations based on various statistical divergences, and clarifies some of the traditional assumptions as arising from the choice of a Bayesian reference prior. Extending also this information-based formalism to cases of concatenated processes, dilated processes and processes with non-Markovian features, both in classical and quantum regimes.

This is a joint work with Valerio Scarani (Centre for Quantum Technologies, National University of Singapore) and Francesco Buscemi (Graduate School of Informatics, Nagoya University).

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[2] C.X. Aw, Francesco Buscemi, V. Scarani “Fluctuation Theorems with Retrodiction rather than Reverse Processes,” AVS Quantum Science 3 045601 (2021).
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