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.

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