  We investigate the qualitative properties of phase transitions in a general
way, if not the single particle numbers of the system but only some particular
charges like e.g. baryon number are conserved. In addition to globally
conserved charges we analyze the implications of locally conserved charge
fractions, like e.g. local electric charge neutrality or locally fixed proton
or lepton fractions. The conditions for phase equilibrium are derived and it is
shown, that the properties of the phase transition do not depend on the locally
conserved fractions. Finally, the general formalism is applied to the
liquid-gas phase transition and the hadron-quark phase transition for typical
astrophysical environments like in supernovae, proto-neutron or a neutron
stars. We demonstrate that the Maxwell construction known from
cold-deleptonized neutron star matter with two locally charge neutral phases
requires modifications and further assumptions concerning the applicability for
hot lepton-rich matter. All possible combinations of local and global
conservation laws are analyzed, and the physical meaningful cases are
identified. Several new kinds of mixed phases are presented, as e.g. a locally
charge neutral mixed phase in proto-neutron stars which will disappear during
the cooling and deleptonization of the proto-neutron star.
