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.
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