Fluctuation theorems with retrodiction rather than reverse processes

Irreversibility is usually captured by a comparison between the process that happens and corresponding "reverse process". In last decades, this has been extensively studied through fluctuation relations. Here we revisit relations from standpoint, suggested decades ago Watanabe, should involve prediction retrodiction on unique process, rather than two processes. We identify necessary sufficient condition for retrodictive reading of relation. The narrative also brings to fore possibility deriving based various statistical divergences, clarifies some traditional assumptions as arising choice reference prior.