A New Method for Derivation of Statistical Weight of the Gentile Statistics

TL;DR

This paper introduces two exact formulas for calculating the statistical weight of Gentile Statistics, improving computational efficiency and extending previous methods to more general cases.

Contribution

It provides a new recursive formula valid for all cases and a combinatoric formula for special cases, enhancing the calculation of Gentile statistical weights.

Findings

Recursive formula is faster than previous methods for large q

Derived formulas applicable to Dai and Xie distribution

Enhanced computational efficiency in statistical weight calculation

Abstract

We present a new method for obtaining the statistical weight of the Gentile Statistics. In a recent paper, Perez and Tun presented an ap- proximate combinatoric and an exact recursive formula for the statistical weight of Gentile Statistics, beginning from bosonic and fermionic cases, respectively [1]. In this paper, we obtain two exact, one combinatoric and one recursive, formulae for the statistical weight of Gentile Statistics, by an another approach. The combinatoric formula is valid only for special cases, whereas recursive formula is valid for all possible cases. Moreover, for a given q-maximum number of particles that can occupy a level for Gentile statistics-the recursive formula we have derived gives the result much faster than the recursive formula presented in [1], when one uses a computer program. Moreover we obtained the statistical weight for the distribution proposed by Dai and Xie in Ref. [2]. Keywords: Fractional statistics, Gentile distribution, Statistical Weight