Mixing and equilibration: Protagonists in the scene of nonextensive statistical mechanics

Abstract

After a brief review of the present status of nonextensive statistical mechanics, we present a conjectural scenario where mixing (characterized by the entropic index $q_{mix}\le 1$) and equilibration (characterized by the entropic index $q_{eq}\ge 1$) play central and inter-related roles, and appear to determine {\it a priori} the values of the relevant indices of the formalism. Boltzmann-Gibbs statistical mechanics is recovered as the $q_{mix}=q_{eq}=1$ particular case.

LaTeX-RevTeX, 28 pages, 7 eps figures, contributed paper to the Proceedings of the International School and Workshop on Nonextensive Thermodynamics and Physical Applications, NEXT 2001, 23-30 May 2001, Cagliari (Italy) (Physica A)

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• The standard map: From Boltzmann-Gibbs statistics to Tsallis statistics
• Nonextensivity and the power-law distributions for the systems with self-gravitating long-range interactions
• Uncertainty relations in terms of Tsallis entropy
• Fluctuations, correlations and the nonextensivity
• Conservative Force Fields in Nonextensive Kinetic Theory
• Derivation of Tsallis statistics from dynamical equations for a granular gas
• Weak insensitivity to initial conditions at the edge of chaos in the logistic map
• Frontier between separability and quantum entanglement in a many spin system
• Collisional cross sections and momentum distributions in astrophysical plasmas: dynamics and statistical mechanics link
• Two-dimensional dissipative maps at chaos threshold: Sensitivity to initial conditions and relaxation dynamics
• Intrinsic Attractive and Repulsive Interactions: From Classical to Quantum Gases in the Generalized Maxwell-Boltzmann Distribution
• Mittag-Leffler Quantum Statistics and Thermodynamic Anomalies