Improved predictions of rare events using the Crooks fluctuation theorem

This article explores the applicability of concepts from nonequilibrium thermodynamics to rare event prediction. The Crooks fluctuation theorem is an equality constraint on the probability distribution of a thermodynamical observable. We consider as a prediction target the exceedance of a threshold of such an observable, where the magnitude of the threshold modulates the rareness of the event. A probability forecast is constructed for this event based on a small observational data set. A simple method is proposed that exploits the Crooks fluctuation theorem to estimate this probability. It is shown that this estimator has improved predictive skill compared to the relative frequency of exceedance in the data set. We quantify this improvement in two examples, and study its dependence on the threshold magnitude and sample size in different systems. Further improvements are achieved by combining the Crooks estimator with the frequency estimator.