{"title":"不同渗流过渡的热力学分析","authors":"Seonghyeon Moon , Young Sul Cho","doi":"10.1016/j.chaos.2025.116491","DOIUrl":null,"url":null,"abstract":"<div><div>This work extends the thermodynamic analysis of random bond percolation to explosive and hybrid percolation models. We show that this thermodynamic analysis is well applicable to both explosive and hybrid percolation models by using the critical exponents <span><math><mi>α</mi></math></span> and <span><math><mi>δ</mi></math></span> obtained from scaling relations with previously measured values of <span><math><mi>β</mi></math></span> and <span><math><mi>γ</mi></math></span> within the error range. As a result, Rushbrooke inequality holds as an equality, <span><math><mrow><mi>α</mi><mo>+</mo><mn>2</mn><mi>β</mi><mo>+</mo><mi>γ</mi><mo>=</mo><mn>2</mn></mrow></math></span>, in both explosive and hybrid percolation models, where <span><math><mrow><mi>α</mi><mo>></mo><mn>0</mn></mrow></math></span> leads to the divergence of specific heats at the critical points. Remarkably, entropy clearly reveals a continuous decrease even in a finite-sized explosive percolation model, unlike the order parameter. In contrast, entropy decreases discontinuously during a discontinuous transition in a hybrid percolation model, resembling the heat outflow during discontinuous transitions in thermal systems.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":"198 ","pages":""},"PeriodicalIF":5.6000,"publicationDate":"2025-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Thermodynamic analysis of diverse percolation transitions\",\"authors\":\"Seonghyeon Moon , Young Sul Cho\",\"doi\":\"10.1016/j.chaos.2025.116491\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>This work extends the thermodynamic analysis of random bond percolation to explosive and hybrid percolation models. We show that this thermodynamic analysis is well applicable to both explosive and hybrid percolation models by using the critical exponents <span><math><mi>α</mi></math></span> and <span><math><mi>δ</mi></math></span> obtained from scaling relations with previously measured values of <span><math><mi>β</mi></math></span> and <span><math><mi>γ</mi></math></span> within the error range. As a result, Rushbrooke inequality holds as an equality, <span><math><mrow><mi>α</mi><mo>+</mo><mn>2</mn><mi>β</mi><mo>+</mo><mi>γ</mi><mo>=</mo><mn>2</mn></mrow></math></span>, in both explosive and hybrid percolation models, where <span><math><mrow><mi>α</mi><mo>></mo><mn>0</mn></mrow></math></span> leads to the divergence of specific heats at the critical points. Remarkably, entropy clearly reveals a continuous decrease even in a finite-sized explosive percolation model, unlike the order parameter. In contrast, entropy decreases discontinuously during a discontinuous transition in a hybrid percolation model, resembling the heat outflow during discontinuous transitions in thermal systems.</div></div>\",\"PeriodicalId\":9764,\"journal\":{\"name\":\"Chaos Solitons & Fractals\",\"volume\":\"198 \",\"pages\":\"\"},\"PeriodicalIF\":5.6000,\"publicationDate\":\"2025-05-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Chaos Solitons & Fractals\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0960077925005041\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Chaos Solitons & Fractals","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0960077925005041","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
Thermodynamic analysis of diverse percolation transitions
This work extends the thermodynamic analysis of random bond percolation to explosive and hybrid percolation models. We show that this thermodynamic analysis is well applicable to both explosive and hybrid percolation models by using the critical exponents and obtained from scaling relations with previously measured values of and within the error range. As a result, Rushbrooke inequality holds as an equality, , in both explosive and hybrid percolation models, where leads to the divergence of specific heats at the critical points. Remarkably, entropy clearly reveals a continuous decrease even in a finite-sized explosive percolation model, unlike the order parameter. In contrast, entropy decreases discontinuously during a discontinuous transition in a hybrid percolation model, resembling the heat outflow during discontinuous transitions in thermal systems.
期刊介绍:
Chaos, Solitons & Fractals strives to establish itself as a premier journal in the interdisciplinary realm of Nonlinear Science, Non-equilibrium, and Complex Phenomena. It welcomes submissions covering a broad spectrum of topics within this field, including dynamics, non-equilibrium processes in physics, chemistry, and geophysics, complex matter and networks, mathematical models, computational biology, applications to quantum and mesoscopic phenomena, fluctuations and random processes, self-organization, and social phenomena.