EOS and phase transition: Nuclei to stars

Abstract : In these lectures we review the present status of knowledge of the nuclear thermal as well as quantum phase transitions. Examples in nuclear physics concern in particular shape transitions, vanishing of pairing correlations at high excitation, nuclear multifragmentation as well as deconfinement to the quark-gluon plasma. For all these phenomena conceptual and formal challenges arise, associated to the definition and classification of phase transitions in finite, open and transient systems. In these lectures we discuss the theoretical methods allowing one to extend the standard formalism of phase transitions to these non-standard situations. The thermodynamics of phase transitions in nuclei is associated to new physics phenomena, very different to the ordinary macroscopic phase transition behaviors. In particular when non-extensive systems as atomic nuclei are subject to of phase transitions, the different statistical ensembles are not equivalent, meaning that the observed physics depends on the externally applied constraints. In this context we show that an extensive external constraint on the order parameter leads to phase separation quenching as well as to thermodynamic anomalies. Two different applications in nuclear physics are worked out, namely the possible occurrence of negative heat capacity in nuclear multifragmentation, and the phase transition quenching in the core-crust transition of neutron stars.