Fluctuation Theorems with Retrodiction rather than Reverse Processes

TL;DR

This paper proposes a novel perspective on fluctuation relations by focusing on retrodiction and prediction within a single process, rather than comparing forward and reverse processes, thus offering new insights into irreversibility and statistical divergences.

Contribution

It introduces a retrodictive framework for fluctuation relations, identifying conditions for their validity and linking them to statistical divergences and reference priors.

Findings

Retrodictive approach generalizes traditional fluctuation relations.

Necessary and sufficient condition for retrodictive fluctuation relations.

Connections between fluctuation relations and statistical divergences.

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.