TY - JOUR

T1 - Extensive Rényi statistics from non-extensive entropy

AU - Parvan, A. S.

AU - Biró, T. S.

PY - 2005/6/13

Y1 - 2005/6/13

N2 - 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.

AB - 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.

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U2 - 10.1016/j.physleta.2005.04.036

DO - 10.1016/j.physleta.2005.04.036

M3 - Article

AN - SCOPUS:19444382575

VL - 340

SP - 375

EP - 387

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

SN - 0375-9601

IS - 5-6

ER -