Statistical mechanics of ideal gas in the presence of minimal length and maximal momentum

TL;DR

This paper investigates how a generalized uncertainty principle with minimal length and maximal momentum alters the thermodynamics of ideal gases, reducing available microstates and affecting their statistical properties.

Contribution

It introduces a modified phase space volume based on GUP and analyzes its impact on the thermodynamics of classical and ultra-relativistic ideal gases.

Findings

Reduction in the total number of microstates

Altered thermodynamic properties of gases

Implications for quantum gravity models

Abstract

Various approaches to quantum gravity suggest that the fundamental volume of the phase space of the given space for representative points, means !0, should be modified. In this paper, we study the effects of this modification on the thermodynamics of an ideal gas within the micro canonical ensemble. For this end, we use a Generalized Uncertainty Principle (GUP) that admits both a minimal measurable length and a maximal momentum. Using this GUP causes decreasing the total number of the microstates of the system. In the first step, we calculate these reductions for classical ideal gas, and in the second step, we calculate these effects for ultra relativistic gas.