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.