  The thermodynamic properties of matter created in high-energy heavy-ion
collisions have been studied in the framework of the non-extensive Tsallis
statistics. The transverse momentum ($p_{\rm T}$)~spectra of identified charged
particles (pions, kaons, protons) and all charged particles from the available
experimental 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 effective
temperature of the thermalized system, respectively. The $p_{\rm T}$~spectra
are well described by the Tsallis distribution function from peripheral to
central collisions for the wide range of collision energies, from $\sqrt{s_{\rm
NN}}$ = 7.7 GeV to 5.02 TeV. The extracted Tsallis parameters are found to be
dependent on the particle species, collision energy, centrality, and fitting
ranges in $p_{\rm T}$. For central collisions, both $q$ and $T$ depend strongly
on 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 from
peripheral to central collisions. For a given centrality, $q$ systematically
increases 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 centrality
shows an anti-correlation between the two parameters.
