The experimental transverse momentum spectra of the charged pions and kaons, protons and antiprotons, produced at midrapidity in [Formula: see text] collisions at [Formula: see text] and 5.02 TeV, central (0–5%) and peripheral (60–80%) Pb[Formula: see text]+[Formula: see text]Pb collisions at [Formula: see text] TeV, central (0–5%), semicentral (40–50%) and peripheral (80–90%) Pb[Formula: see text]+[Formula: see text]Pb collisions at [Formula: see text] TeV, measured by ALICE collaboration, were analyzed using the Tsallis distribution function as well as Hagedorn formula with the embedded transverse flow. To exclude the influence (on the results) of different available fitting [Formula: see text] ranges in the analyzed collisions, we compare the results obtained from combined (simultaneous) fits of midrapidity spectra of the charged pions and kaons, protons and antiprotons with the above theoretical model functions using the identical fitting [Formula: see text] ranges in [Formula: see text] as well as Pb[Formula: see text]+[Formula: see text]Pb collisions at [Formula: see text] and 5.02 TeV. Using the combined fits with the thermodynamically consistent Tsallis distribution as well as the simple Tsallis distribution without thermodynamical description, it is obtained that the global temperature [Formula: see text] and non-extensivity parameter [Formula: see text] slightly increase (consistently for all the particle types) with an increase in center-of-mass (c.m.) energy [Formula: see text] of [Formula: see text] collisions from 2.76 TeV to 5.02 TeV, indicating that the more violent and faster [Formula: see text] collisions at [Formula: see text] TeV result in a smaller degree of thermalization (higher degree of non-equilibrium) compared to that in [Formula: see text] collisions at [Formula: see text] TeV. The [Formula: see text] values for pions and kaons proved to be very close to each other, whereas [Formula: see text] for protons and antiprotons proved to be significantly lower than that for pions and kaons, that is [Formula: see text]. The results of the combined fits using Hagedorn formula with the embedded transverse flow are consistent with practically no (zero) transverse (radial) flow in [Formula: see text] collisions at [Formula: see text] and 5.02 TeV. Using Hagedorn formula with the embedded transverse flow, it is obtained that the value of the (average) transverse flow velocity increases and the temperature [Formula: see text] decreases with an increase in collision centrality in Pb[Formula: see text]+[Formula: see text]Pb collisions at [Formula: see text] and 5.02 TeV, which is in good agreement with the results of the combined Boltzmann–Gibbs blast-wave fits to the particle spectra in Pb[Formula: see text]+[Formula: see text]Pb collisions at [Formula: see text] and 5.02 TeV in recent works of ALICE collaboration. The temperature [Formula: see text] parameter, which approximates the kinetic freeze-out temperature, was shown to coincide in central (0–5%) Pb[Formula: see text]+[Formula: see text]Pb collisions at [Formula: see text] and 5.02 TeV, which implies, taking into account the results of our previous analysis, that kinetic freeze-out temperature stays practically constant in central heavy-ion collisions in [Formula: see text] GeV energy range.

The experimental invariant transverse momentum [Formula: see text] spectra of the charged pions and kaons, protons and antiprotons, produced at midrapidity in central (0–10%) Au[Formula: see text]Au collisions at [Formula: see text], central (0–10%) Cu[Formula: see text]Cu collisions at [Formula: see text], central (0–10%) Au[Formula: see text]Au collisions at [Formula: see text], and central (0–5%) Pb[Formula: see text]Pb collisions at [Formula: see text], measured by BRAHMS, STAR and ALICE collaborations, were analyzed using three different transverse expansion (blast-wave) models: Siemens–Rasmussen blast-wave model, Simple transverse flow model, and Simplified (hydro-inspired) blast-wave model of Schnedermann et al. Combined (simultaneous) minimum [Formula: see text] fits of the experimental invariant [Formula: see text] spectra of the charged pions and kaons, protons and antiprotons with the above three model functions were conducted, using the identical selected optimal fitting ranges in [Formula: see text] in each studied collision system, and the values of the average transverse expansion velocity [Formula: see text] and global kinetic freeze-out temperature [Formula: see text] and their dependencies on the collision system [Formula: see text] and [Formula: see text] were extracted. The combined (simultaneous) fits using Hagedorn formula with the (embedded) simple transverse flow describe well the experimental invariant [Formula: see text] spectra of the charged pions, kaons, protons and antiprotons in the whole measured range in region [Formula: see text] in the analyzed central heavy ion collisions at RHIC and LHC, reproducing qualitatively well all the established dependencies of the parameters [Formula: see text] and [Formula: see text] on the collision system [Formula: see text] and [Formula: see text]. The obtained results were compared with those of the previous analyses of high energy heavy ion collisions.

The midrapidity transverse momentum [Formula: see text] distributions of the charged pions and kaons, protons, and antiprotons, measured by ALICE Collaboration at nine centrality groups of Xe[Formula: see text]Xe collisions at [Formula: see text], have been reproduced quite well using simultaneous (combined) minimum [Formula: see text] fits with the simple (non-consistent) as well as thermodynamically consistent Tsallis function with included transverse flow. The parameters [Formula: see text], [Formula: see text], and [Formula: see text] extracted in this work using both consistent and non-consistent Tsallis function with included transverse flow demonstrate the similar dependencies on collision centrality [Formula: see text]. The obtained non-extensivity parameter [Formula: see text] values decrease systematically for all studied particle species with increasing Xe[Formula: see text]Xe collision centrality, indicating an increase in degree of system thermalization with increasing centrality of heavy-ion collisions. The average transverse flow velocity demonstrates significantly different growth rates in regions [Formula: see text] and [Formula: see text], and parameter [Formula: see text] stays constant within uncertainties in [Formula: see text] range in Xe[Formula: see text]Xe collisions at [Formula: see text]. It is argued that [Formula: see text] could possibly be a threshold border value for a crossover transition from a dense hadronic state to the QGP phase (or mixed phase of QGP and hadrons) in Xe[Formula: see text]Xe collisions at [Formula: see text]. Depletion (enhancement) of [Formula: see text] ratio at low [Formula: see text] (intermediate [Formula: see text]) has been observed in this work in Xe[Formula: see text]Xe collisions at [Formula: see text], which agrees with the similar results of ALICE Collaboration obtained recently in high-energy Xe[Formula: see text]Xe and [Formula: see text] collisions at the LHC. Analyzing and reflecting the extracted [Formula: see text] versus [Formula: see text] and [Formula: see text] versus [Formula: see text] dependencies, we have verified that the depletion (enhancement) of baryon-to-meson ratio at low [Formula: see text] (intermediate [Formula: see text]) values with increasing [Formula: see text] is due to radial flow effects.

The midrapidity transverse momentum distributions of the charged pions, kaons, protons, and antiprotons in ten groups of centrality of Pb+Pb collisions at snn = 2.76 TeV, measured by the ALICE Collaboration, have been analyzed successfully using both thermodynamically consistent and non-consistent Tsallis distribution functions with transverse flow. The collision centrality dependencies of the extracted parameters of two kinds of Tsallis functions with transverse flow have been investigated. The significantly different behavior (growth rates) of ⟨βT⟩ in regions ⟨Npart⟩ < 71 and ⟨Npart⟩ > 71 with the temperature T0 becoming constant in region ⟨Npart⟩ > 71 has been observed. This could indicate that ⟨Npart⟩ = 71±5 (corresponding to ⟨dNch/dη⟩ = 205 ± 15) is a threshold border value of collision centrality for crossover phase transition from the dense hadronic state to the QGP state (or a mixed state of QGP and hadrons) in Pb + Pb collisions at snn = 2.76 TeV. This conjecture is supported further by the observed, significantly different correlations between T0 and ⟨βT⟩ parameters in the corresponding ⟨βT⟩ < 0.44 and ⟨βT⟩ > 0.44 ranges. The strong positive linear correlation between non-extensivity parameter q for pions and kaons, between q for pions and (anti)protons, and between q for kaons and (anti)protons has been obtained. The parameter q for all studied particle species has proven to be strongly anticorrelated with the average transverse flow velocity, ⟨βT⟩. Quite a large positive linear correlation has been obtained between the q of the studied particle species and temperature parameter T0. Analysis of q versus ⟨Npart⟩ dependencies for the studied particle species suggests that the highly thermalized and equilibrated QGP is produced in central Pb + Pb collisions at snn = 2.76 TeV with ⟨Npart⟩ > 160.