{"title":"Analysis of Stochastic Chemical Reaction Networks with a Hierarchy of Timescales","authors":"Lucie Laurence, Philippe Robert","doi":"10.1007/s10955-025-03428-7","DOIUrl":null,"url":null,"abstract":"<div><p>We investigate a class of stochastic chemical reaction networks with <span>\\(n{\\ge }1\\)</span> chemical species <span>\\(S_1\\)</span>, ..., <span>\\(S_n\\)</span>, and whose complexes are only of the form <span>\\(k_iS_i\\)</span>, <span>\\(i{=}1\\)</span>,..., <i>n</i>, where <span>\\((k_i)\\)</span> are integers. The time evolution of these CRNs is driven by the kinetics of the law of mass action. A scaling analysis is done when the rates of external arrivals of chemical species are proportional to a large scaling parameter <i>N</i>. A natural hierarchy of fast processes, a subset of the coordinates of <span>\\((X_i(t))\\)</span>, is determined by the values of the mapping <span>\\(i{\\mapsto }k_i\\)</span>. We show that the scaled vector of coordinates <i>i</i> such that <span>\\(k_i{=}1\\)</span> and the scaled occupation measure of the other coordinates are converging in distribution to a deterministic limit as <i>N</i> gets large. The proof of this result is obtained by establishing a functional equation for the limiting points of the occupation measure, by an induction on the hierarchy of timescales and with relative entropy functions.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":"192 3","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2025-03-10","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://link.springer.com/article/10.1007/s10955-025-03428-7","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
Abstract
We investigate a class of stochastic chemical reaction networks with \(n{\ge }1\) chemical species \(S_1\), ..., \(S_n\), and whose complexes are only of the form \(k_iS_i\), \(i{=}1\),..., n, where \((k_i)\) are integers. The time evolution of these CRNs is driven by the kinetics of the law of mass action. A scaling analysis is done when the rates of external arrivals of chemical species are proportional to a large scaling parameter N. A natural hierarchy of fast processes, a subset of the coordinates of \((X_i(t))\), is determined by the values of the mapping \(i{\mapsto }k_i\). We show that the scaled vector of coordinates i such that \(k_i{=}1\) and the scaled occupation measure of the other coordinates are converging in distribution to a deterministic limit as N gets large. The proof of this result is obtained by establishing a functional equation for the limiting points of the occupation measure, by an induction on the hierarchy of timescales and with relative entropy functions.
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.