The midrapidity transverse momentum distributions of the charged pions, kaons, protons, and antiprotons in ten groups of centrality of Pb + Pb collisions at $\sqrt{s_{nn}}$ = 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 ⟨β_T⟩ in regions $⟨N_{part}⟩$ < 71 and $⟨N_{part}⟩$ > 71 with the temperature T₀ becoming constant in region $⟨N_{part}⟩$ > 71 has been observed. This could indicate that $⟨N_{part}⟩$ = 71 ± 5 (corresponding to $⟨d{N}_{ch}/d\eta ⟩$ = 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 $\sqrt{s_{nn}}$ = 2.76 TeV. This conjecture is supported further by the observed, significantly different correlations between T₀ and $⟨{\beta }_T⟩$ parameters in the corresponding $⟨{\beta }_T⟩$ < 0.44 and $⟨{\beta }_T⟩$ > 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, ⟨β_T⟩. 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 $⟨N_{part}⟩$ dependencies for the studied particle species suggests that the highly thermalized and equilibrated QGP is produced in central Pb + Pb collisions at $\sqrt{s_{nn}}$ = 2.76 TeV with $⟨N_{part}⟩$ > 160.

The midrapidity transverse momentum distributions of the charged pions, kaons, protons, and antiprotons, measured by ALICE Collaboration at ten centrality classes of Pb + Pb collisions at $\sqrt{s_{nn}}$ = 5.02 TeV in the Large Hadron Collider (LHC, CERN, Switzerland), are successfully analyzed using combined minimum χ² fits with a thermodynamically non-consistent, as well as thermodynamically consistent, Tsallis function with transverse flow. The extracted non-extensivity parameter q decreases systematically for all considered particle species with increasing Pb + Pb collision centrality, suggesting an increase in the degree of system thermalization with an increase in collision centrality. The results for q suggest quite a large degree of thermalization of quark–gluon plasma (QGP) created in central Pb + Pb collisions at $\sqrt{s_{nn} }$= 5.02 TeV with the average number of participant nucleons $⟨N_{part}⟩$ > 160. The obtained significantly different growth rates of transverse flow velocity, $⟨{\beta }_T⟩$, in regions $⟨N_{part}⟩$ < 71 ± 7 and $⟨N_{part}⟩$ > 71 ± 7 with the temperature parameter T₀ remaining constant within uncertainties in region $⟨N_{part}⟩$ > 71 ± 7 probably indicates that $⟨N_{part}⟩$ ≈ 71 ± 7 (corresponding to $⟨d{N}_{ch}/d\eta ⟩$ ≈ 251 ± 20) is 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 Pb + Pb collisions at $\sqrt{s_{nn}}$ = 5.02 TeV. The threshold border value for transverse flow velocity $⟨{\beta }_T⟩$ ≈ 0.46 ± 0.03 (corresponding to $⟨N_{part}⟩$ ≈ 71 ± 7), estimated by us in Pb + Pb collisions at $\sqrt{s_{nn}}$ = 5.02 TeV, agrees well with the corresponding border value $⟨{\beta }_T⟩$ ≈ 0.44 ± 0.02, recently obtained in Xe + Xe collisions at $\sqrt{s_{nn} }$= 5.44 TeV, and with almost constant $⟨{\beta }_T⟩$ values extracted earlier in the Beam Energy Scan (BES) program of the Relativistic Heavy-Ion Collider (RHIC, Brookhaven, GA, USA) in central Au + Au collisions in the $\sqrt{s_{nn} }$= 7.7 − 39 GeV energy range, where the threshold for QGP production is achieved. The correlations between extracted T₀ and $⟨{\beta }_T⟩$ parameters are found to be greatly different in regions $⟨{\beta }_T⟩$ < 0.46 and $⟨{\beta }_T⟩$ > 0.46, which further supports our result obtained for the threshold border value in Pb + Pb collisions at $\sqrt{s_{nn}}$= 5.02 TeV.