On the Superstatistical Properties of the Klein-Gordon Oscillator Using Gamma, Log, and F Distributions

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.