{"title":"临界时多组分相互作用系统化学反应的随机分析","authors":"Reda Tiani, Uwe C. Tauber","doi":"10.1209/0295-5075/acff15","DOIUrl":null,"url":null,"abstract":"Abstract We numerically and analytically investigate the behavior of a non-equilibrium phase transition in the second Schlögl autocatalytic reaction scheme. Our model incorporates both an interaction-induced phase separation and a bifurcation in the reaction kinetics, with these critical lines coalescing at a bicritical point in the macroscopic limit. We construct a stochastic master equation for the reaction processes to account for the presence of mutual particle interactions in a thermodynamically consistent manner by imposing a generalized detailed balance condition, which leads to exponential corrections for the transition rates. In a non-spatially extended (zero-dimensional) setting, we treat the interactions in a mean-field approximation, and introduce a minimal model that encodes the physical behavior of the bicritical point and permits the exact evaluation of the anomalous scaling for the particle number fluctuations in the thermodynamic limit. We obtain that the system size scaling exponent for the particle number variance changes from <?CDATA $\\beta _{0} = 3/2$ ?> at the standard non-interacting bifurcation to <?CDATA $\\beta = 12/7$ ?> at the interacting bicritical point. The methodology developed here provides a generic route for the quantitative analysis of fluctuation effects in chemical reactions occurring in multi-component interacting systems.","PeriodicalId":11738,"journal":{"name":"EPL","volume":null,"pages":null},"PeriodicalIF":1.8000,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Stochastic analysis of chemical reactions in multi-component interacting systems at criticality\",\"authors\":\"Reda Tiani, Uwe C. Tauber\",\"doi\":\"10.1209/0295-5075/acff15\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract We numerically and analytically investigate the behavior of a non-equilibrium phase transition in the second Schlögl autocatalytic reaction scheme. Our model incorporates both an interaction-induced phase separation and a bifurcation in the reaction kinetics, with these critical lines coalescing at a bicritical point in the macroscopic limit. We construct a stochastic master equation for the reaction processes to account for the presence of mutual particle interactions in a thermodynamically consistent manner by imposing a generalized detailed balance condition, which leads to exponential corrections for the transition rates. In a non-spatially extended (zero-dimensional) setting, we treat the interactions in a mean-field approximation, and introduce a minimal model that encodes the physical behavior of the bicritical point and permits the exact evaluation of the anomalous scaling for the particle number fluctuations in the thermodynamic limit. We obtain that the system size scaling exponent for the particle number variance changes from <?CDATA $\\\\beta _{0} = 3/2$ ?> at the standard non-interacting bifurcation to <?CDATA $\\\\beta = 12/7$ ?> at the interacting bicritical point. The methodology developed here provides a generic route for the quantitative analysis of fluctuation effects in chemical reactions occurring in multi-component interacting systems.\",\"PeriodicalId\":11738,\"journal\":{\"name\":\"EPL\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.8000,\"publicationDate\":\"2023-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"EPL\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1209/0295-5075/acff15\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"PHYSICS, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"EPL","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1209/0295-5075/acff15","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
Stochastic analysis of chemical reactions in multi-component interacting systems at criticality
Abstract We numerically and analytically investigate the behavior of a non-equilibrium phase transition in the second Schlögl autocatalytic reaction scheme. Our model incorporates both an interaction-induced phase separation and a bifurcation in the reaction kinetics, with these critical lines coalescing at a bicritical point in the macroscopic limit. We construct a stochastic master equation for the reaction processes to account for the presence of mutual particle interactions in a thermodynamically consistent manner by imposing a generalized detailed balance condition, which leads to exponential corrections for the transition rates. In a non-spatially extended (zero-dimensional) setting, we treat the interactions in a mean-field approximation, and introduce a minimal model that encodes the physical behavior of the bicritical point and permits the exact evaluation of the anomalous scaling for the particle number fluctuations in the thermodynamic limit. We obtain that the system size scaling exponent for the particle number variance changes from at the standard non-interacting bifurcation to at the interacting bicritical point. The methodology developed here provides a generic route for the quantitative analysis of fluctuation effects in chemical reactions occurring in multi-component interacting systems.
期刊介绍:
General physics – physics of elementary particles and fields – nuclear physics – atomic, molecular and optical physics – classical areas of phenomenology – physics of gases, plasmas and electrical discharges – condensed matter – cross-disciplinary physics and related areas of science and technology.
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