A system which is disturbed from its equilibrium state will relax toward equilibrium when the associated perturbation is removed. This relaxation process has two characteristic forms in general: (i) damped oscillations, or (ii) monotonic decay. In this section we will be concerned primarily with the latter type of decay (oscillatory responses of bulk superconductors will be discussed in Sec. 54 and are termed collective modes).

Thermodynamic systems have characteristic microscopic (rapid) relaxation times and the relaxation of the vast majority of their internal degrees of freedom proceeds on these time scales. There are two important exceptions: (i) modes involving degrees of freedom for which conservation laws exist; and (ii) additional modes involving a broken symmetry of the system. The conservation laws are those involving mass (or charge), energy (or entropy) and momentum (which, being a vector quantity, involves an equation for each component). For a liquid this leads to the existence of five low frequency (also called hydrodynamic) modes involving: a heat conduction mode (1), transverse viscous shear waves (2), and longitudinal sound (2). The number in parentheses denotes the number of such modes, there being five in all, corresponding to the five conservation laws. For a derivation of this mode structure see Landau and Lifshitz (1987) or Miyano and Ketterson (1979). Additional equations of motion exist when the system spontaneously breaks some symmetry, and we now list some examples.