Gentile statistics with a large maximum occupation number

TL;DR

This paper investigates the thermodynamic properties of Gentile statistics with large maximum occupation numbers, clarifying its relation to Bose-Einstein statistics and emphasizing the role of the ground state, especially for different fugacity regimes.

Contribution

It demonstrates that Gentile statistics only reduces to Bose-Einstein statistics when fugacity is less than one and provides new insights into the ground state contribution and an alternative partition function derivation.

Findings

Gentile statistics converges to Bose-Einstein only for fugacity z<1.

Ground state contribution is significant and previously overlooked.

Provides a detailed thermodynamic analysis of a ν-dimensional Gentile ideal gas.

Abstract

In Gentile statistics the maximum occupation number can take on unrestricted integers: $1<n<\infty $. It is usually believed that Gentile statistics will reduce to Bose-Einstein statistics when n equals the total number of particles in the system N. In this paper, we will show that this statement is valid only when the fugacity z<1; nevertheless, if z>1 the Bose-Einstein case is not recovered from Gentile statistics as n goes to % N . Attention is also concentrated on the contribution of the ground state which was ignored in related literature. The thermodynamic behavior of a $% \nu $-dimensional Gentile ideal gas of particle of dispersion $E=\frac{p^{s}%}{2m}$, where $\nu $ and s are arbitrary, is analyzed in detail. Moreover, we provide an alternative derivation of the partition function for Gentile statistics.