{"title":"On the Superstatistical Properties of the Klein-Gordon Oscillator Using Gamma, Log, and F Distributions","authors":"Soumia Siouane, Abdelmalek Boumali","doi":"10.1007/s10909-024-03224-9","DOIUrl":null,"url":null,"abstract":"<div><p>In this study, we investigate the thermal properties of the relativistic Klein-Gordon oscillator with non-minimal coupling in one, two, and three dimensions within the framework of superstatistics theory. We focus on three distinct distributions: Gamma, Log-Normal, and F-distributions, each described by a specific probability density function <span>\\(f(\\beta )\\)</span>. To compute the partition function, we apply the Euler-MacLaurin formula, incorporating the low-energy asymptotics approximation of superstatistics and accounting for the remainder term <span>\\(R_{i}\\)</span>. Our study involves a detailed analysis of how entropy <span>\\(S\\)</span> and specific heat <span>\\(C_{v}\\)</span> vary with temperature <span>\\(1/\\beta\\)</span> and the universal parameter <span>\\(q\\)</span>, based on the derived partition functions. The variations in these thermodynamic quantities are explored across different dimensionalities and statistical frameworks, providing insights into the interplay between statistical distributions and the thermal dynamics of the system. This approach allows us to understand the influence of non-equilibrium conditions and fluctuating temperature fields on the behavior of relativistic quantum systems. By extending the analysis to multiple dimensions and distribution types, we aim to offer a comprehensive view of how superstatistical distributions affect the thermodynamic properties of the Klein-Gordon oscillator, thus contributing to the broader understanding of thermal dynamics in relativistic systems.</p></div>","PeriodicalId":641,"journal":{"name":"Journal of Low Temperature Physics","volume":"217 Part 4","pages":"598 - 617"},"PeriodicalIF":1.1000,"publicationDate":"2024-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Low Temperature Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s10909-024-03224-9","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"PHYSICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
In this study, we investigate the thermal properties of the relativistic Klein-Gordon oscillator with non-minimal coupling in one, two, and three dimensions within the framework of superstatistics theory. We focus on three distinct distributions: Gamma, Log-Normal, and F-distributions, each described by a specific probability density function \(f(\beta )\). To compute the partition function, we apply the Euler-MacLaurin formula, incorporating the low-energy asymptotics approximation of superstatistics and accounting for the remainder term \(R_{i}\). Our study involves a detailed analysis of how entropy \(S\) and specific heat \(C_{v}\) vary with temperature \(1/\beta\) and the universal parameter \(q\), based on the derived partition functions. The variations in these thermodynamic quantities are explored across different dimensionalities and statistical frameworks, providing insights into the interplay between statistical distributions and the thermal dynamics of the system. This approach allows us to understand the influence of non-equilibrium conditions and fluctuating temperature fields on the behavior of relativistic quantum systems. By extending the analysis to multiple dimensions and distribution types, we aim to offer a comprehensive view of how superstatistical distributions affect the thermodynamic properties of the Klein-Gordon oscillator, thus contributing to the broader understanding of thermal dynamics in relativistic systems.
在本研究中,我们在超统计理论框架内研究了具有非最小耦合的相对论克莱因-戈登振荡器在一维、二维和三维的热特性。我们关注三种不同的分布:伽马分布、对数正态分布和 F 分布,每种分布都由特定的概率密度函数 (f(\beta)\)描述。为了计算分区函数,我们应用了欧拉-麦克劳林公式,结合了超统计的低能渐近近似,并考虑了余项 \(R_{i}\)。我们的研究包括根据推导出的分区函数,详细分析熵(S)和比热(C_{v})如何随温度(1//beta)和通用参数(q)变化。这些热力学量的变化在不同的维度和统计框架下进行了探索,为统计分布和系统热动力学之间的相互作用提供了见解。通过这种方法,我们可以了解非平衡条件和波动温度场对相对论量子系统行为的影响。通过将分析扩展到多个维度和分布类型,我们旨在提供一个关于超统计分布如何影响克莱因-戈登振荡器热力学特性的全面视角,从而有助于更广泛地理解相对论系统的热动力学。
期刊介绍:
The Journal of Low Temperature Physics publishes original papers and review articles on all areas of low temperature physics and cryogenics, including theoretical and experimental contributions. Subject areas include: Quantum solids, liquids and gases; Superfluidity; Superconductivity; Condensed matter physics; Experimental techniques; The Journal encourages the submission of Rapid Communications and Special Issues.