Ultraviolet cut off and Bosonic Dominance

TL;DR

This paper investigates the thermodynamics of a non-interacting gas considering a minimal length uncertainty, highlighting the significant impact of an ultraviolet cutoff and an intrinsic temperature where fermion contributions diminish.

Contribution

It introduces a modified phase space measure and demonstrates the role of an ultraviolet cutoff in thermodynamic properties with a focus on minimal length effects.

Findings

Existence of an intrinsic temperature where fermion contributions vanish

Modified thermodynamic properties due to minimal length and UV cutoff

Ultraviolet cutoff significantly influences phase space and thermodynamics

Abstract

We rederive the thermodynamical properties of a non interacting gas in the presence of a minimal uncertainty in length. Apart from the phase space measure which is modified due to a change of the Heisenberg uncertainty relations, the presence of an ultraviolet cut-off plays a tremendous role. The theory admits an intrinsic temperature above which the fermion contribution to energy density, pressure and entropy is negligible.