Critical Temperature in Nonextensive Hadron Models: A Pressure-based Approach

Abstract

The determination of the critical temperature $T_c$ in strongly interacting matter is central to understanding the transition between confined hadronic matter and deconfined quark-gluon degrees of freedom. In high energy nuclear collisions, intrinsic fluctuations, memory effects, and long-range color interactions can drive the fireball evolution away from purely Markovian thermalization, making nonextensive statistical descriptions relevant near equilibrium. We investigate the critical temperature of nonextensive hadron models using a pressure-based formulation derived from Tsallis entropy. Here we show that the qualitative structure of the pressure equation is controlled by both the nonextensive parameter $q$ and the model-dependent bag contribution $B^{\text{model}}$. For $q=0$, the pressure equations are monotonic and admit a unique positive root, whereas for $q=1$ the seventh-order term vanishes and analytic solutions can be obtained. For $q>1$, the negative $T^7$ contribution modifies the pressure behavior and can generate multiple positive roots at finite volume. %Cosmological bounds require $q\approx 1$, meaning $q\simeq 1.001$ in proton-proton phenomenology is a system-dependent fit parameter. For $q\ge 1$, $T_c^{\text{model}}$ is $\left(102.3\le T_c^{\text{MIT}}\le 106.1,86.5\le T_c^{\text{Dual}}\le 87.8,\text{and}113.1\le T_c^{\text{Fuzzy}}\le 121.1\right)$ MeV. At $q=0$, $T_c^{\text{model}}\sim 55$ MeV marks the nuclear liquid-gas transition. A weighted comparison constrained by the MIT bag model at $q=1$ gives $(T_c^{\text{w}}\approx 102)\text{MeV}$, with Fuzzy and Dual QCD terms entering as model-propagation corrections. The interval $(0.99\le q\le 1.002)$ therefore provides the most reliable domain for a common physical interpretation and a composite estimate of the critical temperature.

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