A Note on Effects of Generalized and Extended Uncertainty Principles on Juttner Gas

In recent years, the implications of the generalized (GUP) and extended (EUP) uncertainty principles 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 Juttner 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 Juttner 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.

Automated summary

The implications of GUP and EUP on a system following the Juttner distribution are investigated in this study, with a focus on deriving the distribution function from the partition function and its relation to thermal energy to ultimately determine the corresponding energy density states.