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Zbl 1145.82303
Parvan, A.S.; Biró, T.S.
Extensive Rényi statistics from non-extensive entropy. (English)
[J] Phys. Lett., A 340, No. 5-6, 375-387 (2005). ISSN 0375-9601

Summary: We show that starting with either the non-extensive Tsallis entropy in Wang's formalism or the extensive Rényi entropy, it is possible to construct equilibrium non-Gibbs canonical distribution functions which satisfy the fundamental equations of thermodynamics. The statistical mechanics with Tsallis entropy does not satisfy the zeroth law of thermodynamics at dynamical and statistical independence request, whereas the extensive Rényi statistics fulfills all requirements of equilibrium thermodynamics in the microcanonical ensemble. Transformation formulas between Tsallis statistics in Wang representation and Rényi statistics are presented. The one-particle distribution function in Rényi statistics for a classical ideal gas at finite particle number has a power-law tail for large momenta.

MSC 2000:: *82B03 Foundations of equilibrium statistical mechanics
82-02 Research monographs (statistical mechanics)
94A17 Measures of information

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