bibkey: “roldan2015arrow” authors: “Édgar Roldán; Izaak Neri; Meik Dörpinghaus; Heinrich Meyr; Frank Jülicher” year: 2015 title: “Decision Making in the Arrow of Time” doi: “10.1103/PhysRevLett.115.250602” url: “https://doi.org/10.1103/PhysRevLett.115.250602” claim: “Forward-versus-reversed path testing uses the path log-likelihood ratio; the stated sequential mean decision-time identity assumes a continuous likelihood process and includes an excess term.” strata_touched: [] license: “citation-only” triage: “anchor”

Decision Making in the Arrow of Time

Physical Review Letters 115, 250602 (2015), page 250602-2, equations (1)–(6). The publisher’s full text identifies the forward/reversed path likelihood ratio with the entropy-change functional. Equation (4) gives a mean sequential decision time for continuous log-likelihood paths, including the excess term defined in equation (5). Page 250602-4 discusses discontinuous jumps in the illustrative chemical model and the resulting limitations of the small-error bound.

This is literature-attested background for path likelihood and sequential decision times. It is not used to infer a fixed-horizon Bayes error from a KL rate. The parity-kernel results instead derive their current formula and dimension-dependent Poisson error curve directly. This note records no priority claim for those deductions.

Primary text: https://harvest.aps.org/v2/journals/articles/10.1103/PhysRevLett.115.250602/fulltext.