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

Research output: Contribution to journalArticlepeer-review

Izaak Neri, Matteo Polettini

Original languageEnglish
Number of pages41
JournalSciPost Physics
Accepted/In press30 Mar 2023


  • 2208.02839

    2208.02839.pdf, 880 KB, application/pdf

    Uploaded date:12 Apr 2023

    Version:Accepted author manuscript

    Licence:CC BY

King's Authors


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.

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