Implications of Minimal Length Scale on the Statistical Mechanics of Ideal Gas

TL;DR

This paper explores how a minimal length scale, suggested by quantum gravity theories, modifies the phase space volume and thermodynamics of an ideal gas, potentially offering experimental insights into quantum gravity.

Contribution

It introduces a novel momentum-dependent modification to phase space volume and analyzes its impact on ideal gas thermodynamics within the GUP framework.

Findings

Modified phase space affects thermodynamic properties at quantum gravity scales

Potential experimental signatures of quantum gravity effects in ideal gas behavior

Supports the relevance of quantum gravity proposals through thermodynamic modifications

Abstract

Several alternative approaches to quantum gravity problem suggest the modification of the {\it fundamental volume $\omega_{0}$} of the accessible phase space for representative points. This modified fundamental volume has a novel momentum dependence. In this paper, we study the effects of this modification on the thermodynamics of an ideal gas within the microcanonical ensemble and using the generalized uncertainty principle(GUP). Although the induced modifications are important only in quantum gravity era, possible experimental manifestation of these effects may provides strong support for underlying quantum gravity proposal.