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

Author

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  • Martı́nez, S
  • Pennini, F
  • Plastino, A
  • Portesi, M

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.

Suggested Citation

  • Martı́nez, S & Pennini, F & Plastino, A & Portesi, M, 2004. "q-thermostatistics and the analytical treatment of the ideal Fermi gas," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 332(C), pages 230-248.
  • Handle: RePEc:eee:phsmap:v:332:y:2004:i:c:p:230-248
    DOI: 10.1016/j.physa.2003.10.026
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    Cited by:

    1. Montani, Fernando & Phoka, Elena & Portesi, Mariela & Schultz, Simon R., 2013. "Statistical modelling of higher-order correlations in pools of neural activity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(14), pages 3066-3086.
    2. Rovenchak, Andrij & Sobko, Bohdana, 2019. "Fugacity versus chemical potential in nonadditive generalizations of the ideal Fermi-gas," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).

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