Extending Cercignani’s Conjecture Results from Boltzmann to Boltzmann–Fermi–Dirac Equation

IF 1.3 3区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL
Thomas Borsoni
{"title":"Extending Cercignani’s Conjecture Results from Boltzmann to Boltzmann–Fermi–Dirac Equation","authors":"Thomas Borsoni","doi":"10.1007/s10955-024-03262-3","DOIUrl":null,"url":null,"abstract":"<div><p>We establish a connection between the relative Classical entropy and the relative Fermi–Dirac entropy, allowing to transpose, in the context of the Boltzmann or Landau equation, any entropy–entropy production inequality from one case to the other; therefore providing entropy–entropy production inequalities for the Boltzmann–Fermi–Dirac operator, similar to the ones of the Classical Boltzmann operator. We also provide a generalized version of the Csiszár–Kullback–Pinsker inequality to weighted <span>\\(L^p\\)</span> norms, <span>\\(1 \\le p \\le 2\\)</span> and a wide class of entropies.</p></div>","PeriodicalId":667,"journal":{"name":"Journal of Statistical Physics","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2024-04-27","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/s10955-024-03262-3","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 establish a connection between the relative Classical entropy and the relative Fermi–Dirac entropy, allowing to transpose, in the context of the Boltzmann or Landau equation, any entropy–entropy production inequality from one case to the other; therefore providing entropy–entropy production inequalities for the Boltzmann–Fermi–Dirac operator, similar to the ones of the Classical Boltzmann operator. We also provide a generalized version of the Csiszár–Kullback–Pinsker inequality to weighted \(L^p\) norms, \(1 \le p \le 2\) and a wide class of entropies.

将塞西尼亚尼猜想的结果从玻尔兹曼扩展到玻尔兹曼-费米-狄拉克方程
我们在相对经典熵和相对费米-狄拉克熵之间建立了联系,从而可以在玻尔兹曼方程或朗道方程的背景下,将任何熵-熵生成不等式从一种情况转置到另一种情况;因此为玻尔兹曼-费米-狄拉克算子提供了熵-熵生成不等式,类似于经典玻尔兹曼算子的熵-熵生成不等式。我们还提供了Csiszár-Kullback-Pinsker不等式的广义版本,它适用于加权\(L^p\)规范、\(1 \le p \le 2\) 和一大类熵。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
Journal of Statistical Physics
Journal of Statistical Physics 物理-物理:数学物理
CiteScore
3.10
自引率
12.50%
发文量
152
审稿时长
3-6 weeks
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.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信