2009/09/29 by Jun Ohkubo · 14 citations
Economics, Econometrics and Finance · Physics and Astronomy · #Bayes' theorem #Fluctuation theorem #Generalization #Probability theory #Quantum Mechanics and Applications #Stochastic process #Stochastic processes and financial applications #cond-mat.stat-mech #stochastic dynamics and bifurcation
paper · pdf · doi:10.1143/jpsj.78.123001
published in Journal of the Physical Society of Japan 78(12), 123001 (Physical Society of Japan) · 4 pages
arxiv created 2009/09/29 · openalex publication_date 2009/11/25 · arxiv updated 2015/05/14 · openalex created_date 2019/06/27 · openalex updated_date 2026/08/05
A generalization of fluctuation theorems in stochastic processes is proposed. The new theorem is written in terms of posterior probabilities, which are introduced via the Bayes theorem. In usual fluctuation theorems, a forward path and its time reversal play an important role, so that a microscopically reversible condition is essential. In contrast, the microscopically reversible condition is not necessary in the new theorem. It is shown that the new theorem adequately recovers various theorems and relations previously known, such as the Gallavotti-Cohen-type fluctuation theorem, the Jarzynski equality, and the Hatano-Sasa relation, when adequate assumptions are employed.