  Tsallis Statistics was used to investigate the non-Boltzmann distribution of
particle spectra and their dependence on particle species and beam energy in
the relativistic heavy-ion collisions at SPS and RHIC. Produced particles are
assumed to acquire radial flow and be of non-extensive statistics at
freeze-out. J/psi and the particles containing strangeness were examined
separately to study their radial flow and freeze-out. We found that the strange
hadrons approach equilibrium quickly from peripheral to central A+A collisions
and they tend to decouple earlier from the system than the light hadrons but
with the same final radial flow. These results provide an alternative picture
of freeze-outs: a thermalized system is produced at partonic phase; the
hadronic scattering at later stage is not enough to maintain the system in
equilibrium and does not increase the radial flow of the copiously produced
light hadrons. The J/psi in Pb+Pb collisions at SPS is consistent with early
decoupling and obtains little radial flow. The J/psi spectra at RHIC are also
inconsistent with the bulk flow profile.
