Ultraviolet cut off and Bosonic Dominance

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.