Abstract
A model of low-frequency relaxation in condensed matter is provided. The model involves time-dependent transition rates which are obtained from time-independent transition rates. The time dependence arises because of an environment that provides a time-dependent entropy contribution to the free energy that controls the transitions. The model has two related consequences. Firstly, relaxations at low frequencies conform in general to a fractional exponential decay function, phi = phi 0 exp(-(t/ tau p)1-n), 0<or=n<1, independent of both the nature of primary relaxation species and the type of condensed matter. This fractional exponential decay property of relaxation has been widely verified. The general occurrence of this behaviour allows a confident determination of the key parameter, n, in the fractional exponential decay function, to be made. A second consequence of the model is the concept that the relaxation time tau p observed in a particular experiment is related to a direct relaxation time tau 0 that would occur in a time-independent environment by means of a relation dependent on the same key parameter n determined from the relaxation measurement. The latter relation provides various renormalisation relations appropriate to particular situations.