Low-frequency relaxation in condensed matter and the evolution of entropy

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), 0p 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.