A Note on Effects of Generalized and Extended Uncertainty Principles on J\"{u}ttner Gas

TL;DR

This paper investigates how generalized and extended uncertainty principles influence the Jüttner distribution, a relativistic extension of Maxwell-Boltzmann statistics, by deriving the distribution from the partition function and energy density states.

Contribution

It introduces a method to analyze the effects of GUP and EUP on systems obeying the Jüttner distribution, extending prior work beyond classical Maxwell-Boltzmann statistics.

Findings

Derived modified distribution functions under GUP and EUP

Analyzed the impact on relativistic energy states

Provided a framework for future relativistic statistical mechanics studies

Abstract

In recent years, the implications of the generalized (GUP) and extended (EUP) uncertainty prin-ciples on Maxwell-Boltzmann distribution have been widely investigated. However, at high energy regimes, the validity of Maxwell-Boltzmann statistics is under debate and instead, the J\"{u}ttner distribution is proposed as the distribution function in relativistic limit. Motivated by these considerations, in the present work, our aim is to study the effects of GUP and EUP on a system that obeys the J\"{u}ttner distribution. To achieve this goal, we address a method to get the distribution function by starting from the partition function and its relation with thermal energy which finally helps us in finding the corresponding energy density states.