Based on general thermodynamic relationships, the types of phase transitions available for implementation in intense waves of isentropic compression and expansion, as well as in powerful shock waves are considered. Consideration assumes only the presence of local thermodynamic equilibrium in the system. The proposed formalism is used to study dynamic methods of melting, high-temperature boiling and plasma phase transitions. Depending on the thermodynamic features of the substance, thermodynamic conditions for the occurrence of shock rupture instabilities in a medium with an arbitrary equation of state are formulated. For a wide range of specialists involved in applied physics and new technology, as well as for all physicists and mechanics interested in modern physics of high energy densities.