q-thermostatistics and the analytical treatment of the ideal Fermi gas

TL;DR

This paper explores the exact q-thermostatistical framework for an ideal Fermi gas, deriving the generalized partition function and occupation numbers for arbitrary q, and analyzing limiting cases and their relation to traditional Fermi-Dirac statistics.

Contribution

It provides the first exact formulation of the q-thermostatistics for an ideal Fermi system, extending the conventional Fermi-Dirac statistics to nonextensive cases.

Findings

Derived the generalized partition function for arbitrary q

Analyzed high- and low-temperature regimes in the thermodynamic limit

Compared q-thermostatistics results with traditional Fermi-Dirac statistics

Abstract

We discuss relevant aspects of the exact q-thermostatistical treatment for an ideal Fermi system. The grand canonical exact generalized partition function is given for arbitrary values of the nonextensivity index q, and the ensuing statistics is derived. Special attention is paid to the mean occupation numbers of single-particle levels. Limiting instances of interest are discussed in some detail, namely, the thermodynamic limit, considering in particular both the high- and low-temperature regimes, and the approximate results pertaining to the case q \sim 1 (the conventional Fermi-Dirac statistics corresponds to q=1). We compare our findings with previous Tsallis' literature.