As the density of matter increases, atomic nuclei disintegrate into nucleons and, eventually, the nucleons themselves disintegrate into quarks. The phase transitions (PTs) between these phases can vary from steep first order to smooth crossovers, depending on certain conditions. First-order PTs with more than one globally conserved charge, so-called non-congruent PTs, have characteristic differences compared to congruent PTs. In this conference proceeding we discuss the non-congruence of the quark deconfinement PT at high densities and/or temperatures relevant for heavy-ion collisions, neutron stars, proto-neutron stars, supernova explosions, and compact-star mergers.
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