Eur. Phys. J. A (2025) 61: 156
https://doi.org/10.1140/epja/s10050-025-01626-1

Regular Article - Theoretical Physics

Thermodynamic analysis of transverse momentum spectra in Pb–Pb collisions at 2.76 TeV: centrality dependence of temperature, freezeout parameters and non-extensitivity

¹ Hubei Key Laboratory of Energy Storage and Power Battery, School of Optoelectronic Engineering, School of New Energy, Hubei University of Automotive Technology, 442002, Shiyan, China
² Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apartado Postal 70-543, 04510, Mexico City, Mexico
³ Department of Physics, Abdul Wali Khan University Mardan, 23200, Mardan, Pakistan
⁴ Department of Computer Sciences, Faculty of Computing and Information Technology, Northern Border University, 91911, Rafha, Saudi Arabia
⁵ Department of Physics, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, 11671, Riyadh, Saudi Arabia
⁶ College of Humanities and Sciences, Ajman University, P.O. Box 346, Ajman, United Arab Emirates

^a waqas_phy313@yahoo.com, 20220073@huat.edu.cn

Received: 26 January 2025
Accepted: 18 June 2025
Published online: 10 July 2025

Abstract

We study properties of Pb–Pb collisions at 2.76 TeV in mid-rapidity, $|y|<0.5,$ based on data by the ALICE Collaboration. In particular, we examine the transverse momentum $(p_T)$ spectra of positively charged (identified) hadrons, ${\pi }^{+},$$K^{+}$ and p,  generated in various centrality intervals. We perform individual fits using the thermodynamically consistent Tsallis distribution to extract the following quantities: the non-extensitivity parameter, q,  the effective temperature, $T_{\text{eff}},$ the kinetic freezeout volume, V,  the mean transverse flow velocity, ${\beta }_T,$ the mean kinetic freezeout temperature, $⟨T_0⟩,$ the thermal temperature, $T_{\text{th}},$ and the parameter $\zeta ,$ which characterizes the fluctuating number of generated particles. From peripheral to central collision, and from lower to higher charged particle multiplicity per pseudorapidity unit, $⟨d{N}_{\text{ch}}/d\eta ⟩,$ all these quantities are observed to increase, with the exception of q,  which has the opposite behavior. The parameters $T_{\text{eff}},$q,  and V depend on the hadron mass in a way that supports the scenarios of volume differential freezeout and multiple kinetic freezeout. Furthermore, we extracted $⟨T_{\text{eff}}⟩$ and $⟨q⟩$ for different collisions and energies at LHC and RHIC, and compare their dependencies on $⟨d{N}_{\text{ch}}/d\eta ⟩$ and $⟨N_{\text{part}}⟩.$