Decision Making in the Arrow of Time

TL;DR

This paper establishes a quantitative link between entropy production rate and the minimal decision time to determine the arrow of time in stochastic processes, using optimal statistical tests and fluctuation theorems.

Contribution

It introduces a method to estimate entropy production from first-passage times and derives a fluctuation theorem relating decision times for correct and wrong inferences.

Findings

Entropy production rate is inversely proportional to decision time.

Decision time distributions for correct and wrong decisions are equal.

Method demonstrated through numerical simulations of nonequilibrium processes.

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.