Non-dissipative flows in many-particle systems as a consequence of symmetry breaking

It is shown that there may exist undamped flows in many particle systems which are in thermodynamic equilibrium spatially inhomogeneous states with broken symmetries. If the thermodynamic potential of a system is invariant with respect to some transformation depending on continuous parameters, then to this transformation correspond the densities of conserving flows and the integrals of motion, the number of which is equal to that of continuous parameters of the transformation. The stability of the superconducting and superfluid flows, the onset of which is a consequence of the phase symmetry breakdown, is explained by the conservation law which allows no breakdown of these states not adequate to an absolute minimum of the thermodynamic potential