Chemical and mechanical instability in warm and dense nuclear matter

We investigate the possible thermodynamic instability in a warm and dense nuclear medium (T <= 50 MeV and rho(0) <= rho(B) <= 3 rho(0)) where a phase transition from nucleonic matter to resonance-dominated Delta matter can take place. The analysis is performed by requiring the global conservation of baryon and electric charge numbers in the framework of a relativistic equation of state. Similarly to the liquid-gas phase transition, we show that the nucleon-Delta matter phase transition is characterized by both mechanical instability (fluctuations on the baryon density) and by chemical-diffusive instability (fluctuations on the charge concentration) in asymmetric nuclear matter. We then perform an investigation and a comparative study on the different nature of such instabilities and phase transitions.