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The thermodynamic properties of matter created in high-energy heavy-ioncollisions have been studied in the framework of the non-extensive Tsallisstatistics. The transverse momentum ($p_{\rm T}$)~spectra of identified chargedparticles (pions, kaons, protons) and all charged particles from the availableexperimental data of Au-Au collisions at the Relativistic Heavy Ion Collider(RHIC) energies and Pb-Pb collisions at the Large Hadron Collider (LHC)energies are fitted by the Tsallis distribution. The fit parameters, $q$ and$T$ measure the degree of deviation from an equilibrium state and the effectivetemperature of the thermalized system, respectively. The $p_{\rm T}$~spectraare well described by the Tsallis distribution function from peripheral tocentral collisions for the wide range of collision energies, from $\sqrt{s_{\rmNN}}$ = 7.7 GeV to 5.02 TeV. The extracted Tsallis parameters are found to bedependent on the particle species, collision energy, centrality, and fittingranges in $p_{\rm T}$. For central collisions, both $q$ and $T$ depend stronglyon the fit ranges in $p_{\rm T}$. For most of the collision energies, $q$remains almost constant as a function of centrality, whereas $T$ increases fromperipheral to central collisions. For a given centrality, $q$ systematicallyincreases as a function of collision energy whereas $T$ has a decreasing trend.A profile plot of $q$ and $T$ with respect to collision energy and centralityshows an anti-correlation between the two parameters.

Centrality, transverse momentum and collision energy dependence of the Tsallis parameters in relativistic heavy-ion collisions