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Decision Making in the Arrow of Time

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Edgar Roldan, Izaak Neri, Heinrich Doerpinghaus, Frank Juelicher

Original languageEnglish
Article number250602
Number of pages5
JournalPhysical Review Letters
Early online date16 Dec 2015
Accepted/In press15 Nov 2015
E-pub ahead of print16 Dec 2015


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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.

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