  We propose that transverse momentum spectra with power-law tails observed in
ultrarelativistic heavy ion collisions can be interpreted as originating in a
medium in thermal equilibrium. General conditions on the dynamical equations
are formulated, leading in equilibrium to various energy distributions of
particles. Starting with the linear Fokker-Planck equation we analyze
conditions for Boltzmann-Gibbs, Tsallis, or other equilibrium distributions
based upon the dependence of fluctuation and dissipation on the energy of the
observed subsystem. RHIC neutral pion data definitely exclude Boltzmann-Gibbs
distribution over the entire range of observed transverse momenta.
