Abstract. Based on the quasi-particle description of the QCD medium at finite temperature and density we formulate the phenomenological model for the equation of state that exhibits crossover or the first order deconfinement phase transition. The models are constructed in such a way to be thermodynamically consistent and to satisfy the properties of the ground state nuclear matter comply with constraints from intermediate heavy-ion collision data. Our equations of states show quite reasonable agreement with the recent lattice findings on temperature and baryon chemical potential dependence of relevant thermodynamical quantities in the parameter range covering both the hadronic and quark-gluon sectors. The model predictions on the isentropic trajectories in the phase diagram are shown to be consistent with the recent lattice results. Our nuclear equations of states are to be considered as an input to the dynamical models describing the production and the time evolution of a thermalized medium created in heavy ion collisions in a broad energy range from SIS up to LHC.PACS. 21.65.+f Nuclear matter -24.85.+p Quarks, gluons, and QCD in nuclei and nuclear processes -12.38.Aw General properties of QCD -12.38.Mh Quark-gluon plasma

No abstract

The shear (η) and bulk (ζ) viscosities are calculated in a quasiparticle relaxation time approximation. The hadron phase is described within the relativistic mean field based model with scaled hadron masses and couplings. The quark phase is treated in terms of the heavy quark bag model fitted to the lattice data. A twophase model allowing for the first order phase transition from the hadron phase to the strongly coupled quark gluon plasma is constructed by means of the Gibbs conditions. Temperature and baryon density dependence of the calculated viscosityto-entropy ratios (η/s, ζ/s) are analyzed and compared with those obtained in other models. Special attention is paid to the behavior of viscosity coefficients near the critical temperature, from both hadron and quark-gluon side. Effects of resonance widths on viscosities and viscosity-to-entropy ratios are estimated.