Two-fluid hydrodynamic description of ordered systems

A unified description of systems with a condensed phase in terms of hydrodynamic equations of motion is given. These equations are of two kinds: First those equations obeyed by the thermal excitations (the "first fluid") typically are local conservation equations of mass, energy and momentum. Second the equation obeyed by the condensed phase (the "second fluid") is an equation of motion related to the order parameter of the broken symmetry. These equations are established on phenomenological grounds making use of irreversible thermodynamics. The eigenmodes of the linearized form of these equations, typically first and second sound, are discussed in particular with respect to their manifestation in inelastic light and neutron scattering. The systems considered are homogenous superfluids, superconductors, dielectric crystals and magnetic systems. Except for superfluid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ the critical behavior at the phase transition to the ordered state is not systematically discussed.