Universality of kappa distributions

IF 1.8 4区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY
EPL Pub Date : 2024-06-02 DOI:10.1209/0295-5075/ad4415
George Livadiotis and David J. McComas
{"title":"Universality of kappa distributions","authors":"George Livadiotis and David J. McComas","doi":"10.1209/0295-5075/ad4415","DOIUrl":null,"url":null,"abstract":"This paper reveals the universality of the particle energy distribution function, despite the arbitrariness that characterizes the generalized thermodynamic entropic function. We show that the canonical distribution, that is, the distribution function that maximizes this entropy under the constraints of canonical ensemble, is always the same and given by the kappa distribution function. We use the recently developed entropy defect to express the generalized entropic formulation. The entropy defect is a thermodynamic concept that describes the loss of entropy due to the order induced by the presence of correlations. Then we carry out functional analysis to maximize the implicit expression of the generalized entropy. Critically, we show that the Lagrange multipliers have the same exact arbitrariness as the generalized entropic function, allowing us to cancel it out and proving the universality of canonical distribution as the kappa distribution function.","PeriodicalId":11738,"journal":{"name":"EPL","volume":"310 1","pages":""},"PeriodicalIF":1.8000,"publicationDate":"2024-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"EPL","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1209/0295-5075/ad4415","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}
引用次数: 0

Abstract

This paper reveals the universality of the particle energy distribution function, despite the arbitrariness that characterizes the generalized thermodynamic entropic function. We show that the canonical distribution, that is, the distribution function that maximizes this entropy under the constraints of canonical ensemble, is always the same and given by the kappa distribution function. We use the recently developed entropy defect to express the generalized entropic formulation. The entropy defect is a thermodynamic concept that describes the loss of entropy due to the order induced by the presence of correlations. Then we carry out functional analysis to maximize the implicit expression of the generalized entropy. Critically, we show that the Lagrange multipliers have the same exact arbitrariness as the generalized entropic function, allowing us to cancel it out and proving the universality of canonical distribution as the kappa distribution function.
卡帕分布的普遍性
尽管广义热力学熵函数具有任意性,但本文揭示了粒子能量分布函数的普遍性。我们证明了典型分布,即在典型集合约束下使该熵最大化的分布函数,总是相同的,并由卡帕分布函数给出。我们使用最近开发的熵缺陷来表达广义熵公式。熵缺陷是一个热力学概念,它描述了由于相关性的存在而引起的有序熵损失。然后,我们进行函数分析,最大化广义熵的隐式表达。重要的是,我们证明了拉格朗日乘数与广义熵函数具有完全相同的任意性,从而可以将其抵消,并证明了卡帕分布函数的典型分布的普遍性。
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
EPL
EPL 物理-物理:综合
CiteScore
3.30
自引率
5.60%
发文量
332
审稿时长
1.9 months
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. Letters submitted to EPL should contain new results, ideas, concepts, experimental methods, theoretical treatments, including those with application potential and be of broad interest and importance to one or several sections of the physics community. The presentation should satisfy the specialist, yet remain understandable to the researchers in other fields through a suitable, clearly written introduction and conclusion (if appropriate). EPL also publishes Comments on Letters previously published in the Journal.
×
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