title: Decision Making in the Arrow of Time.
abstract: We show that the steady-state entropy production rate of a stochastic process is inversely proportional to the minimal time needed to decide on the direction of the arrow of time. Here we apply Wald's sequential probability ratio test to optimally decide on the direction of time's arrow in stationary Markov processes. Furthermore, the steady-state entropy production rate can be estimated using mean first-passage times of suitable physical variables. We derive a first-passage time fluctuation theorem which implies that the decision time distributions for correct and wrong decisions are equal. Our results are illustrated by numerical simulations of two simple examples of nonequilibrium processes.
authors.affiliation: Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany.|Center for Advancing Electronics Dresden, 01062 cfaed, Germany.
authors.forename: Édgar
authors.initials: É
authors.lastname: Roldán
authors.affiliation: Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany.|Max Planck Institute of Molecular Cell Biology and Genetics, Pfotenhauerstraße 108, 01307 Dresden, Germany.|Center for Advancing Electronics Dresden, 01062 cfaed, Germany.
authors.forename: Izaak
authors.initials: I
authors.lastname: Neri
authors.affiliation: Vodafone Chair Mobile Communications Systems, Technische Universität Dresden, 01062 Dresden, Germany.|Center for Advancing Electronics Dresden, 01062 cfaed, Germany.
authors.forename: Meik
authors.initials: M
authors.lastname: Dörpinghaus
authors.affiliation: Vodafone Chair Mobile Communications Systems, Technische Universität Dresden, 01062 Dresden, Germany.|Institute for Integrated Signal Processing Systems, RWTH Aachen University, 52056 Aachen, Germany.|Center for Advancing Electronics Dresden, 01062 cfaed, Germany.
authors.forename: Heinrich
authors.initials: H
authors.lastname: Meyr
authors.affiliation: Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany.|Center for Advancing Electronics Dresden, 01062 cfaed, Germany.
authors.forename: Frank
authors.initials: F
authors.lastname: Jülicher
mesh_terms: D019277:Entropy; D008390:Markov Chains; D008962:Models, Theoretical