A generalization of the quantum van der Waals equation of state for a multi-component system in the grand canonical ensemble is proposed. The model includes quantum statistical effects and allows to specify the parameters characterizing repulsive and attractive forces for each pair of particle species.The model can be straightforwardly applied to the description of asymmetric nuclear matter and also for mixtures of interacting nucleons and nuclei. Applications of the model to the equation of state of an interacting hadron resonance gas are discussed.

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 µB = 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 − µB-plane. The deviations from the free ideal hadron gas baseline at µB = 0 and T ≈ 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 µB ≈ 1.5 GeV, and at even higher baryon densities µB ≈ 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 µB neutron stars as well as the new neutron star merger observations. The effective EoS presented here describes simultaneously lattice QCD results at µB = 0, as well as observed physical phenomena (nuclear matter and neutron star matter) at T ∼ = 0 and high densities, µB > 1 GeV.