Extreme value statistics of edge currents in Markov jump processes and their use for entropy production estimation

TL;DR

This paper uses martingale theory to analyze the extreme value statistics of edge currents in Markov jump processes, enabling more accurate estimation of entropy production from limited observational data.

Contribution

It introduces a novel approach to estimate entropy production using the extreme value distribution of edge currents, applicable with partial information from a marginal observer.

Findings

Infima of integrated edge currents are geometrically distributed.

A marginal observer can estimate a finite fraction of entropy production.

Extreme value-based estimates of dissipation are more accurate than traditional methods.

Abstract

The infimum of an integrated current is its extreme value against the direction of its average flow. Using martingale theory, we show that the infima of integrated edge currents in time-homogeneous Markov jump processes are geometrically distributed, with a mean value determined by the effective affinity measured by a marginal observer that only sees the integrated edge current. In addition, we show that a marginal observer can estimate a finite fraction of the average entropy production rate in the underlying nonequilibrium process from the extreme value statistics in the integrated edge current. The estimated average rate of dissipation obtained in this way equals the above mentioned effective affinity times the average edge current. Moreover, we show that estimates of dissipation based on extreme value statistics can be significantly more accurate than those based on thermodynamic uncertainty ratios, as well as those based on a naive estimator obtained by neglecting nonMarkovian correlations in the Kullback-Leibler divergence of the trajectories of the integrated edge current.