接触模型的熵产生

IF 2.2 3区物理与天体物理 Q2 MECHANICS

Journal of Statistical Mechanics: Theory and Experiment Pub Date : 2024-09-09 DOI:10.1088/1742-5468/ad72db

Tânia Tomé, Mário J de Oliveira

{"title":"接触模型的熵产生","authors":"Tânia Tomé, Mário J de Oliveira","doi":"10.1088/1742-5468/ad72db","DOIUrl":null,"url":null,"abstract":"We propose an expression for the production of entropy for a system described by a stochastic dynamics which is appropriate for the case where the reverse transition rate vanishes but the forward transition is nonzero. The expression is positive definite and based on the inequality <inline-formula>\n<tex-math><?CDATA $x\\ln x-(x-1)\\unicode{x2A7E}0$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:mi>x</mml:mi><mml:mi>ln</mml:mi><mml:mo>⁡</mml:mo><mml:mi>x</mml:mi><mml:mo>−</mml:mo><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>x</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy=\"false\">)</mml:mo><mml:mtext>⩾</mml:mtext><mml:mn>0</mml:mn></mml:mrow></mml:math><inline-graphic xlink:href=\"jstatad72dbieqn1.gif\"></inline-graphic></inline-formula>. The corresponding entropy flux is linear in the probability distribution allowing its calculation as an average. The expression is applied to the one-dimensional contact process at the stationary state. We found that the rate of entropy production per site is finite with a singularity at the critical point with diverging slope.","PeriodicalId":17207,"journal":{"name":"Journal of Statistical Mechanics: Theory and Experiment","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Entropy production of the contact model\",\"authors\":\"Tânia Tomé, Mário J de Oliveira\",\"doi\":\"10.1088/1742-5468/ad72db\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We propose an expression for the production of entropy for a system described by a stochastic dynamics which is appropriate for the case where the reverse transition rate vanishes but the forward transition is nonzero. The expression is positive definite and based on the inequality <inline-formula>\\n<tex-math><?CDATA $x\\\\ln x-(x-1)\\\\unicode{x2A7E}0$?></tex-math><mml:math overflow=\\\"scroll\\\"><mml:mrow><mml:mi>x</mml:mi><mml:mi>ln</mml:mi><mml:mo>⁡</mml:mo><mml:mi>x</mml:mi><mml:mo>−</mml:mo><mml:mo stretchy=\\\"false\\\">(</mml:mo><mml:mi>x</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy=\\\"false\\\">)</mml:mo><mml:mtext>⩾</mml:mtext><mml:mn>0</mml:mn></mml:mrow></mml:math><inline-graphic xlink:href=\\\"jstatad72dbieqn1.gif\\\"></inline-graphic></inline-formula>. The corresponding entropy flux is linear in the probability distribution allowing its calculation as an average. The expression is applied to the one-dimensional contact process at the stationary state. We found that the rate of entropy production per site is finite with a singularity at the critical point with diverging slope.\",\"PeriodicalId\":17207,\"journal\":{\"name\":\"Journal of Statistical Mechanics: Theory and Experiment\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.2000,\"publicationDate\":\"2024-09-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Statistical Mechanics: Theory and Experiment\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1088/1742-5468/ad72db\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MECHANICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Statistical Mechanics: Theory and Experiment","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1088/1742-5468/ad72db","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MECHANICS","Score":null,"Total":0}

引用次数: 0

摘要

我们提出了一个随机动力学描述系统的熵产生表达式，它适用于反向转换率消失但正向转换率不为零的情况。该表达式为正定式，基于不等式 xlnx-(x-1)⩾0。相应的熵通量在概率分布中是线性的，可以平均计算。该表达式适用于静止状态下的一维接触过程。我们发现，每个点的熵产生率是有限的，在临界点存在一个斜率发散的奇点。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Entropy production of the contact model

We propose an expression for the production of entropy for a system described by a stochastic dynamics which is appropriate for the case where the reverse transition rate vanishes but the forward transition is nonzero. The expression is positive definite and based on the inequality

xln⁡x−(x−1)⩾0

. The corresponding entropy flux is linear in the probability distribution allowing its calculation as an average. The expression is applied to the one-dimensional contact process at the stationary state. We found that the rate of entropy production per site is finite with a singularity at the critical point with diverging slope.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Journal of Statistical Mechanics: Theory and Experiment 物理-力学

CiteScore

4.50

自引率

12.50%

发文量

210

审稿时长

1.0 months

期刊介绍： JSTAT is targeted to a broad community interested in different aspects of statistical physics, which are roughly defined by the fields represented in the conferences called ''Statistical Physics''. Submissions from experimentalists working on all the topics which have some ''connection to statistical physics are also strongly encouraged. The journal covers different topics which correspond to the following keyword sections. 1. Quantum statistical physics, condensed matter, integrable systems Scientific Directors: Eduardo Fradkin and Giuseppe Mussardo 2. Classical statistical mechanics, equilibrium and non-equilibrium Scientific Directors: David Mukamel, Matteo Marsili and Giuseppe Mussardo 3. Disordered systems, classical and quantum Scientific Directors: Eduardo Fradkin and Riccardo Zecchina 4. Interdisciplinary statistical mechanics Scientific Directors: Matteo Marsili and Riccardo Zecchina 5. Biological modelling and information Scientific Directors: Matteo Marsili, William Bialek and Riccardo Zecchina