Time-scaling in irreversible thermodynamics

We consider linear dynamical systems with motions characterized by two different time-scales. In practice the dynamical matrix in the phenomenological equations of motion often exhibits a strong coupling of the slow and fast variables. It is shown on the basis of the Onsager symmetry relations that a simple transformation of variables leads to a weak coupling. After the transformation one can use perturbation theory to derive reduced matrices describing the slow (fast) motions of the slow (fast) subsystem.