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

Matteo Polettini; Izaak Neri

doi:10.1007/s10955-024-03236-5

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arXiv · 2208.02888

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

Matteo Polettini·Izaak Neri

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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.

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Matteo Polettini, Izaak Neri. 2022-08-04. Multicyclic norias: a first-transition approach to extreme values of the currents. https://doi.org/10.1007/s10955-024-03236-5

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