The thermodynamic properties of high temperature and high density QCD-matter are explored within the Chiral SU ( 3 ) -flavor parity-doublet Polyakov-loop quark-hadron mean-field model , CMF .
The quark sector of the CMF model is tuned to describe the \mu _ { B } = 0 thermodynamics data of lattice QCD .
The resulting lines of constant physical variables as well as the baryon number susceptibilities are studied in some detail in the temperature/chemical potential plane .
The CMF model predicts three consecutive transitions , the nuclear first-order liquid-vapor phase transition , chiral symmetry restoration , and the cross-over transition to a quark-dominated phase .
All three phenomena are cross-over , for most of the T - \mu _ { B } -plane .
The deviations from the free ideal hadron gas baseline at \mu _ { B } = 0 and T \approx 100 - 200 MeV can be attributed to remnants of the liquid-vapor first order phase transition in nuclear matter .
The chiral crossing transition determines the baryon fluctuations at much higher \mu _ { B } \approx 1.5 GeV , and at even higher baryon densities \mu _ { B } \approx 2.4 GeV , the behavior of fluctuations is controlled by the deconfinement cross-over .
The CMF model also describe well the static properties of high \mu _ { B } neutron stars as well as the new neutron star merger observations .
The effective EoS presented here describes simultaneously lattice QCD results at \mu _ { B } = 0 , as well as observed physical phenomena ( nuclear matter and neutron star matter ) at T \cong 0 and high densities , \mu _ { B } > 1 GeV .