  We propose that power-law tailed hadron spectra may be viewed as stemming
from a matter in an unconventional equilibrium state typical for non-extensive
thermodynamics. A non-extensive Boltzmann equation, which is able to form such
spectra as a stationary solution, is utilized as a rough model of quark matter
hadronization. Basic ideas about non-extensive simulation of the QCD equation
of state on the lattice are presented.
