QCD phase transition at finite temperature and chemical potential with the non-extensive statistics

The intrinsic fluctuations, memory effects and long-range color interactions in high energy nuclear collisions imply the presence of non-Markovian processes in the fireball evolution, which affects the thermalization process towards equilibrium and produces a non-extensive behavior. In order to investigate the non-equilibrium effect on the quantum chromodynamics (QCD) phase transition at finite temperature ($T$) and chemical potential ($\mu$), we apply a non-extensive correction to the equation of state in the parton (hadron resonance) gas at high (low) temperature and interpolate these two equation of states with a smooth crossover. The non-extensive statistics is characterized by a non-extensivity parameter $q$, which measures the degrees of deviation from the thermal equilibrium. It is found that the dimensionless thermodynamic quantities such as the entropy density, the pressure, the energy density, the specific heat at constant volume and the trace anomaly are sensitive to the deviation of $q$ from unity and they become large both in the hadronic and quark-gluon plasma phases with the increase of $q$. Moreover, this deviation leads to nontrivial corrections of the squared speed of sound ($(c_s^2)_q$) in the vicinity of the critical point ($T_c$) and at lower temperatures. Additionally, these thermodynamic quantities are sensitive to the deviation of $\mu$ from zero. With increasing $\mu$, they become enhanced in both phases. Specifically, for $(c_s^2)_q$, the value increases near $T_c$ but decreases at lower temperatures. Finally, we observe that our results with $q=1$ agree well with those from the Lattice QCD, the hadron resonance gas model, and the Thermal-Fist fit to the hadron yields in high energy nuclear collisions in the low temperature region up to $T\sim 150$ MeV.