Multicyclic norias: a first-transition approach to extreme values of the currents
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866929272339300352 |
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| author | Polettini, Matteo Neri, Izaak |
| author_facet | Polettini, Matteo Neri, Izaak |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2208_02888 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Multicyclic norias: a first-transition approach to extreme values of the currents Polettini, Matteo Neri, Izaak Statistical Mechanics 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. |
| title | Multicyclic norias: a first-transition approach to extreme values of the currents |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2208.02888 |