David J McComas, George Livadiotis, Nicholas V Sarlis
{"title":"Correlations and Kappa Distributions: Numerical Experiment and Physical Understanding.","authors":"David J McComas, George Livadiotis, Nicholas V Sarlis","doi":"10.3390/e27040375","DOIUrl":null,"url":null,"abstract":"<p><p>Kappa distributions, their statistical framework, and their thermodynamic origin describe systems with correlations among their particle energies, residing in stationary states out of classical thermal equilibrium/space plasmas, from solar wind to the outer heliosphere, are such systems. We show how correlations from long-range interactions compete with collisions to define the specific shape of particle velocity distributions, using a simple numerical experiment with collisions and a variable amount of correlation among the particles. When the correlations are turned off, collisions drive any initial distribution to evolve toward equilibrium and a Maxwell-Boltzmann (MB) distribution. However, when some correlation is introduced, the distribution evolves toward a different stationary state defined by a kappa distribution with some finite value of the thermodynamic kappa κ (where κ→∞ corresponds to a MB distribution). Furthermore, the stronger the correlations, the lower the κ value. This simple numerical experiment illuminates the role of correlations in forming stationary state particle distributions, which are described by kappa distributions, as well as the physical interpretation of correlations from long-range interactions and how they are related to the thermodynamic kappa.</p>","PeriodicalId":11694,"journal":{"name":"Entropy","volume":"27 4","pages":""},"PeriodicalIF":2.1000,"publicationDate":"2025-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12025533/pdf/","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Entropy","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.3390/e27040375","RegionNum":3,"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
Kappa distributions, their statistical framework, and their thermodynamic origin describe systems with correlations among their particle energies, residing in stationary states out of classical thermal equilibrium/space plasmas, from solar wind to the outer heliosphere, are such systems. We show how correlations from long-range interactions compete with collisions to define the specific shape of particle velocity distributions, using a simple numerical experiment with collisions and a variable amount of correlation among the particles. When the correlations are turned off, collisions drive any initial distribution to evolve toward equilibrium and a Maxwell-Boltzmann (MB) distribution. However, when some correlation is introduced, the distribution evolves toward a different stationary state defined by a kappa distribution with some finite value of the thermodynamic kappa κ (where κ→∞ corresponds to a MB distribution). Furthermore, the stronger the correlations, the lower the κ value. This simple numerical experiment illuminates the role of correlations in forming stationary state particle distributions, which are described by kappa distributions, as well as the physical interpretation of correlations from long-range interactions and how they are related to the thermodynamic kappa.
期刊介绍:
Entropy (ISSN 1099-4300), an international and interdisciplinary journal of entropy and information studies, publishes reviews, regular research papers and short notes. Our aim is to encourage scientists to publish as much as possible their theoretical and experimental details. There is no restriction on the length of the papers. If there are computation and the experiment, the details must be provided so that the results can be reproduced.