In this paper, we investigate the kinetic freeze-out properties in relativistic heavy ion collisions at different collision energies. We present a study of standard Boltzmann-Gibbs Blast-Wave (BGBW) fits and Tsallis Blast-Wave (TBW) fits performed on the transverse momentum spectra of identified hadrons produced in Au + Au collisions at collision energies of $sqrt{s_{rm{NN}}}=$ 7.7 - 200 GeV at the Relativistic Heavy Ion Collider (RHIC), and in Pb + Pb collisions at collision energies of $sqrt{s_{rm{NN}}}=$ 2.76 and 5.02 TeV at the Large Hadron Collider (LHC). The behavior of strange and multi-strange particles is also investigated. We found that the TBW model describes data better than the BGBW one overall, and the contrast is more prominent as the collision energy increases as the degree of non-equilibrium of the produced system is found to increase. From TBW fits, the kinetic freeze-out temperature at the same centrality shows a weak dependence of collision energy between 7.7 and 39 GeV, while it decreases as collision energy continues to increase up to 5.02 TeV. The radial flow is found to be consistent with zero in peripheral collisions at RHIC energies but sizable at LHC energies and central collisions at all RHIC energies. We also observed that the strange hadrons, with higher temperature and similar radial flow, approach equilibrium more quickly from peripheral to central collisions than light hadrons. The dependence of temperature and flow velocity on non-equilibrium parameter ($q-1$) is characterized by two second-order polynomials. Both $a$ and $dxi$ from the polynomials fit, related to the influence of the system bulk viscosity, increase toward lower RHIC energies.
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