Nonlinear nuclear equation of state and thermodynamical instabilities in warm and dense nuclear matter

We study a nonlinear nuclear equation of state in the framework of a relativistic mean field theory. We investigate the possible thermodynamic instability in a warm and dense asymmetric nuclear medium where a phase transition from nucleonic matter to resonance dominated Δ matter can take place. Such a phase transition is characterized by both mechanical instability (fluctuations on the baryon density) and by chemical-diffusive instability (fluctuations on the isospin concentration) in asymmetric nuclear matter. Similarly to the liquid-gas phase transition, the nucleonic and the Δ-matter phase have a different isospin density in the mixed phase. In the liquid-gas phase transition, the process of producing a larger neutron excess in the gas phase is referred to as isospin fractionation. A similar effects can occur in the nucleon-Δ matter phase transition due essentially to a negative Δ-particles excess in asymmetric nuclear matter. In this context, we investigate also the effects of power law effects, due to the possible presence of nonextensive statistical mechanics effects.