Multicyclic norias: a first-transition approach to extreme values of the currents

Abstract

For continuous-time Markov chains we prove that, depending on the notion of effective affinity $F$, the probability of an edge current to ever become negative is either $1$ if $F<0$ else $\sim \exp -F$. The result generalizes a ``noria'' formula to multicyclic networks. We give operational insights on the effective affinity and compare several estimators, arguing that stopping problems may be more accurate in assessing the nonequilibrium nature of a system according to a local observer. Finally we elaborate on the similarity with the Boltzmann formula. The results are based on a constructive first-transition approach.

25 pages, 2 figures

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