Softening of the equation of state of matter at large densities and temperatures: Chiral symmetry restoration vs. quark deconfinement

We discuss two models for describing the behavior of matter at large densities and intermediate temperatures. In both models a softening of the equation of state takes place due to the appearance of new degrees of freedom. The first is a hadronic model in which the softening is due to chiral symmetry restoration. In the second model the softening is associated with the formation of clusters of quarks in the mixed phase. We show that both models allow a significant softening but, in the first case the bulk modulus is mainly dependent on the density, while in the mixed phase model it also strongly depends on the temperature. We also show that the bulk modulus is not vanishing in the mixed phase due to the presence of two conserved charges, the baryon and the isospin one. Only in a small region of densities and temperatures the incompressibility becomes extremely small. Finally we compare our results with recent analysis of heavy ion collisions at intermediate energies.