Relaxation processes with age-dependent transition rates

In order to explain the experimental fact that the relaxation function for many systems is not a simple exponential function of time, a number of theories in which the transition rates of the responding elements from one state to another are time-dependent have been proposed recently. However, in many cases these transition rates will often depend not on the absolute time but on the time since the last transition, i.e., the age of the state. Moreover, the initial distribution of ages must be that appropriate to the definition of the relaxation function. As an example of the importance of these considerations, the appropriate formalism is presented for a simple system of dipoles, and the results of calculations for a specific form of the transition rate for time-dependent and age-dependent rates are compared.