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

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 ∼ 1 (the conventional Fermi–Dirac statistics corresponds to q = 1). We compare our findings with previous Tsallis’ literature.