Multiplicity dependencies of midrapidity [Formula: see text] spectra of identified charged particles in inelastic [Formula: see text] collisions at [Formula: see text] TeV at the Large Hadron Collider (LHC), measured by ALICE Collaboration, have been analyzed. The combined minimum [Formula: see text] fits with thermodynamically consistent Tsallis function as well as Hagedorn function with the embedded transverse flow describe quite satisfactorily the [Formula: see text] spectra of particles in the studied 10 different classes of charged-particle multiplicity in inelastic [Formula: see text] collisions at [Formula: see text] TeV. The obtained effective temperatures [Formula: see text] of thermodynamically consistent Tsallis function demonstrate a consistent growth with an increase in multiplicity of charged particles in inelastic [Formula: see text] collisions at [Formula: see text] TeV, and the corresponding [Formula: see text] versus the average charged-particle (pseudorapidity) multiplicity density [Formula: see text] dependence is described very well by the simple power function with exponent parameter [Formula: see text] (1/3) in the whole analyzed range [Formula: see text]. It is found that the transverse (radial) flow becomes significant at higher multiplicity events in [Formula: see text] collisions at [Formula: see text] TeV, reaching the maximum value [Formula: see text] at the largest studied multiplicity density [Formula: see text]. It is estimated from analysis of [Formula: see text] and [Formula: see text] versus [Formula: see text] dependencies, obtained using Hagedorn function with the embedded transverse flow, that the probable onset of deconfinement phase transition in inelastic [Formula: see text] collisions at [Formula: see text] TeV occurs at [Formula: see text].

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, 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.

Dependencies of midrapidity pt distributions of the charged pions and kaons, protons and antiprotons on charged-particle multiplicity density (<dNch/dη>) in inelastic proton-proton collisions at (s)1/2 = 7 TeV at the LHC, measured by ALICE Collaboration, are investigated. The simultaneous minimum χ2 fits with the Tsallis function with thermodynamical consistence and the Hagedorn function with included transverse flow have well-described the pt spectra of the particle species in the ten studied groups of charged-particle multiplicity density. The effective temperatures, T, of the Tsallis function with thermodynamical consistence have shown a steady rise with increasing the charged-particle multiplicity in proton-proton collisions at (s)1/2 = 7 TeV, in agreement with the similar result obtained recently in proton-proton collisions at (s)1/2 = 13 TeV at the LHC. The respective T versus <dNch/dη> dependence in proton-proton collisions at (s)1/2 = 7 TeV is reproduced quite well by the simple power function with the same value (≈ 1/3) of the exponent parameter as that extracted in proton-proton collisions at (s)1/2 = 13 TeV. The identical power dependence T~ε1/3 between the initial energy density and effective temperature of the system has been observed in proton-proton collisions at (s)1/2 = 7 and 13 TeV. We have observed that the transverse radial flow emerges at <dNch/dη> ≈ 6 and then increases, becoming substantial at larger multiplicity events in proton-proton collisions at (s)1/2 = 7 TeV. We have estimated, analyzing T0 and ⟨βt⟩ versus <dNch/dη> dependencies, that the possible onset of deconfinement phase transition in proton-proton collisions at (s)1/2 = 7 TeV occurs at <dNch/dη> ≈ 6.1 ± 0.3, which is close to the corresponding recent estimate (<dNch/dη> ≈ 7.1 ± 0.2) in proton-proton collisions at (s)1/2 = 13 TeV. The corresponding critical energy densities for probable onset of deconfinement phase transition in proton-proton collisions at (s)1/2 = 7 and 13 TeV at the LHC have been estimated to be 0.67 ± 0.03 and 0.76 ± 0.02 GeV/fm3, respectively.

The experimental spectra of [Formula: see text] versus the average pseudorapidity multiplicity density, [Formula: see text], and [Formula: see text] dependencies of the identified charged particles at midrapidity in Au[Formula: see text]Au and Pb[Formula: see text]Pb collisions at RHIC and LHC in (s[Formula: see text]-5020[Formula: see text]GeV energy range are described well with the proposed simple power model function. The degree of flattening of [Formula: see text] of the charged pions and kaons, protons and antiprotons in the analyzed heavy-ion collisions at RHIC and LHC in (s[Formula: see text]-5020[Formula: see text]GeV energy range are investigated analyzing the dependencies of the obtained exponent parameter [Formula: see text] of the simple power model function on the particle species and collision energy (s[Formula: see text]. The coincidence of the parameter [Formula: see text] for pions and kaons in Pb[Formula: see text]Pb collisions at (s[Formula: see text][Formula: see text]TeV, reflecting practically identical shapes of [Formula: see text] versus the average pseudorapidity multiplicity density, [Formula: see text], and [Formula: see text] spectra for pions and kaons in these collisions, is obtained. This important result is interpreted as due to creation of the highly thermalized QGP, where the difference between [Formula: see text], [Formula: see text] and [Formula: see text] flavors practically disappears, resulting in similar mechanisms of production of pions and kaons in Pb[Formula: see text]Pb collisions at (s[Formula: see text][Formula: see text]TeV.