Abstract
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. Here, we revisit fluctuation relations from the standpoint, suggested decades ago by Watanabe, that the comparison should involve the prediction and the retrodiction on the unique process, rather than two processes. We identify a necessary and sufficient condition for a retrodictive reading of a fluctuation relation. 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 reference prior.
Highlights
In the pursuit of this line of research, we recognize that our previous paper was not radical enough
The retrodictive narrative 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 reference prior
We compare the fluctuation relations obtained in the retrodictive narrative with those obtained in the reverse-process narrative
Summary
Quantitative approaches to irreversibility traditionally involve a comparison between the process physically happening, usually called forward process, and a corresponding reverse (or backward) process. We proposed to define the reverse process in terms of Bayesian retrodiction. The replacement of irreversibility with irretrodictability was pioneered by Watanabe, though prior to our previous work no connection had been drawn with the fluctuation theorems derived in the last twenty years. Under this change of viewpoint, it is the same physics that is being described, freed from an excess baggage in the narrative (and possibly, on the interpretation). We have adopted a compact approach to references: besides those that prove specific results, we shall cite mostly reference books and reviews, and occasionally a few works that we consider clear and exemplary, useful as entry points for the reader, without any expectation of being exhaustive
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