Two generalizations of the Boltzmann equation

Abstract

We connect two different generalizations of Boltzmann's kinetic theory by requiring the same stationary solution. Non-extensive statistics can be produced by either using corresponding collision rates nonlinear in the one-particle densities or equivalently by using nontrivial energy composition rules in the energy conservation constraint. Direct transformation formulas between key functions of the two approaches are given.

Talk given at the 3rd NEXT-Sigma-Phi Conference, Crete, Aug.2005, revtex, 10 page, 2 figs

References in corpus (4)

• Statistical mechanics in the context of special relativity II
• Two-parameter deformations of logarithm, exponential, and entropy: A consistent framework for generalized statistical mechanics
• Non-extensive Boltzmann Equation and Hadronization
• Generalized Fokker-Planck equations and effective thermodynamics

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