Thermodynamic properties and phase diagram of quark matter within non-extensive Polyakov chiral SU(3) quark mean field model

In the present study,we applied Tsallis non-extensive statistics to investigate the thermodynamic properties and phase diagram of quark matter in the Polyakov chiral SU（3） quark mean field model.Within this model,the properties of the quark matter were modified through the scalar fields σ,ξ,δ,χ,vector fields ω,ρ,φ,and Polyakov fields Φ and Φat finite temperature and chemical potential.Non-extensive effects were introduced through a dimensionless parameter q,and the results were compared to those of the extensive case（q→1）.In the non-extensive case,the exponential in the Fermi-Dirac（FD） function was modified to a q-exponential form.The influence of the q parameter on the thermodynamic properties,pressure,energy,and entropy density,as well as trace anomaly,was investigated.The speed of sound and specific heat with non-extensive effects were also studied.Furthermore,the effeet of non-extensivity on the deconfinement phase transition as well as the chiral phase transition of u,d,and s quarks was explored.We found that the critical end point（CEP）,which defines the point in the（T-μ） phase diagram where the order of the phase transition changes,shifts to a lower value of temperature,TCEP,and a higher value of chemical potential,μCEP, as the non-extensivity is increased,that is,q>1.