  For a general, associative addition rule defining a non-extensive
thermodynamics we construct the strict monotonic function, which transforms it
to an additive quantity. We investigate the evolution of one-particle
distributions in the framework of a two-body Boltzmann equation supported with
a non-extensive energy addition rule. In particular we study the emergence of a
Tsallis distribution as a stationary solution. We propose that for describing
the hadronization of quark matter non-extensive rules may apply.
