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

Abstract

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 Jüttner 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 Jüttner 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.

Symmetry in Quantum Theory of Gravity

“…The paper of Moradpour, Aghababaei, and Ziaie examines the effects of generalizing the uncertainty principle from a different perspective, computing the behavior of both the Maxwell-Boltzmann distribution and its relativistic extension, the Jüttner distribution, as the long-range curvature effects are increased [15]. As expected, long-range corrections have a smaller effect on the Jüttner distribution; however, and consistent with the above, they remain far outside the bounds of current observational capabilities.…”

Minimal length implications on the Hartree–Fock theory

“…In order to calculate the effects of the minimal length on the energy of the electron liquid in metals, one must use [20,24]…”

Generalized uncertainty principle and burning stars

“…Indeed, the existence of a minimal length leads to the emergence of the GUP (Hossenfelder, 2013), and it affects thermodynamics (Chang et al, 2002;Fityo, 2008;Wang et al, 2010;Hossenfelder, 2013;Motlaq and Pedram, 2014;Moradpour et al, 2021) and quantum mechanics (Kempf et al, 1995;Kempf, 1996), as P can be expanded as a function of p. This letter deals with the GUP effects on star burning facilitated by quantum tunneling. Loosely speaking, we investigate the effects of a minimal length on T (the Gamow temperature).…”

“…There have been various attempts to estimate the maximum possible upper bound on β 0 (Zhu et al, 2009;Chemissany et al, 2011;Das and Mann, 2011;Sprenger et al, 2011;Pikovski et al, 2012;Husain et al, 2013;Ghosh, 2014;Jalalzadeh et al, 2014;Scardigli and Casadio, 2015;Bosso et al, 2017;Feng et al, 2017;Gecim and Sucu, 2017;Bushev et al, 2019;Luciano and Petruzziello, 2019;Park, 2020;Aghababaei et al, 2021;Feleppa et al, 2021;Mohammadi Sabet et al, 2021), and among them, it seems that the maximum estimation for the upper bound is of the order of 10 78 (Scardigli and Casadio, 2015). The implications of GUP on stellar evolution (Moradpour et al, 2019;Shababi and Ourabah, 2020) and the thermodynamics of various gases (Chang et al, 2002;Fityo, 2008;Wang et al, 2010;Hossenfelder, 2013;Motlaq and Pedram, 2014;Moradpour et al, 2021) have also been studied.…”