Extreme value statistics of edge currents in Markov jump processes

Izaak Neri, Matteo Polettini

Published 2022-08-04Version 1

The infimum of a current is its extreme value against the direction of its average flow. We show that the probability mass function of the infima of edge currents in time-homogeneous Markov jump processes is that of a geometric distribution, with a mean value determined by the effective affinity measured by a marginal observer that only sees the edge current. In addition, we show that a marginal observer can estimate the average entropy production rate of the underlying nonequilibrium process from the extreme value statistics in the 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 and Kullback-Leibler divergences.