Speed distribution of relativistic one-dimensional Gentile particles in a box

We show the morphological transition in the speed distribution for identical particles in a 1D infinite well. By including the relativistic dispersion relation in numerical calculations for particles following Gentile statistics, we recover the Maxwell-Jüttner distribution. Our results show that the transition to the relativistic case occurs at lower critical temperature for fermions than for bosons. For systems with intermediate statistics, this transition occurs at temperatures between these two limits.