{"title":"多环 Norias:电流极值的第一过渡法","authors":"Matteo Polettini, Izaak Neri","doi":"10.1007/s10955-024-03236-5","DOIUrl":null,"url":null,"abstract":"<p>For continuous-time Markov chains we prove that, depending on the notion of effective affinity <i>F</i>, the probability of an edge current to ever become negative is either 1 if <span>\\(F< 0\\)</span> else <span>\\(\\sim \\exp - F\\)</span>. 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.</p>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2024-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Multicyclic Norias: A First-Transition Approach to Extreme Values of the Currents\",\"authors\":\"Matteo Polettini, Izaak Neri\",\"doi\":\"10.1007/s10955-024-03236-5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>For continuous-time Markov chains we prove that, depending on the notion of effective affinity <i>F</i>, the probability of an edge current to ever become negative is either 1 if <span>\\\\(F< 0\\\\)</span> else <span>\\\\(\\\\sim \\\\exp - F\\\\)</span>. 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.</p>\",\"PeriodicalId\":667,\"journal\":{\"name\":\"Journal of Statistical Physics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2024-03-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Statistical Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1007/s10955-024-03236-5\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"PHYSICS, MATHEMATICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Statistical Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1007/s10955-024-03236-5","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
摘要
对于连续时间马尔可夫链,我们证明,根据有效亲和力 F 的概念,边电流变为负值的概率为 1 if \(F< 0\) else \(\sim \exp - F\).这一结果将 "诺里亚 "公式推广到了多环网络。我们给出了关于有效亲和力的操作见解,并比较了几种估计方法,认为停止问题在根据局部观察者评估系统的非平衡性质时可能更准确。最后,我们阐述了与玻尔兹曼公式的相似性。这些结果都是基于建设性的第一过渡方法得出的。
Multicyclic Norias: A First-Transition Approach to Extreme Values of the Currents
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.
期刊介绍:
The Journal of Statistical Physics publishes original and invited review papers in all areas of statistical physics as well as in related fields concerned with collective phenomena in physical systems.