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 = 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 = 5.02 TeV with the average number of participant nucleons > 160. The obtained significantly different growth rates of transverse flow velocity, , in regions < 71 ± 7 and > 71 ± 7 with the temperature parameter T0 remaining constant within uncertainties in region > 71 ± 7 probably indicates that ≈ 71 ± 7 (corresponding to ≈ 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 = 5.02 TeV. The threshold border value for transverse flow velocity ≈ 0.46 ± 0.03 (corresponding to ≈ 71 ± 7), estimated by us in Pb + Pb collisions at = 5.02 TeV, agrees well with the corresponding border value ≈ 0.44 ± 0.02, recently obtained in Xe + Xe collisions at = 5.44 TeV, and with almost constant values extracted earlier in the Beam Energy Scan (BES) program of the Relativistic Heavy-Ion Collider (RHIC, Brookhaven, USA) in central Au + Au collisions in the = 7.7 − 39 GeV energy range, where the threshold for QGP production is achieved. The correlations between extracted T0 and parameters are found to be greatly different in regions < 0.46 and > 0.46, which further supports our result obtained for the threshold border value in Pb + Pb collisions at = 5.02 TeV.

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.

An approach for measuring the energy of high-energy particles by a thin calorimeter, is presented. The method is based on the universality in the development of cascade processes. For measurements of the primary energy of cosmic ray particles, the correlation analysis of the dependence of the number of secondary particles, N e , at the observation level and the relation of the number of particles, d N , at two levels, divided by an absorber layer, is used. It is shown, that the use of correlation curves (logN e versus d N ) allows to essentially reduce errors in determining the energy of the primary particle, which are connected with the uncertainty in the nature of the primary nucleus and with fluctuations in the development of the cascade process. Uncertainties of energy reconstruction on the basis of the correlation curves methodology, is less than 10 percent.