FLUCTUATION-DISSIPATION RELATIONS AND UNIVERSAL BEHAVIOR FOR RELAXATION PROCESSES IN SYSTEMS WITH STATIC DISORDER AND IN THE THEORY OF MORTALITY

A unified description for the parallel relaxation in systems with stat ic disorder and for the competitive risk mortality theory in populatio n biology is suggested by combining the physical and biological approa ches presented in the literature. A multichannel parallel decay proces s is investigated by assuming that each channel is characterized by a state vector x and by a probability of decaying p(x;t). A general fluc tuation-dissipation relation is derived which relates the effective de cay rate of the process to the fluctuations of the density of channels characterized by different state vectors. A limit of the thermodynami c type in x space is introduced for which both the volume available an d the average number of channels tend to infinity, but the average vol ume density of channels remains constant. By using scaling arguments c ombined with a stochastic renormalization group approach, two types of universal laws are identified in the thermodynamic limit for the rela xation (survival) function corresponding to nonintermittent and interm ittent fluctuations of the density of channels, respectively, For noni ntermittent fluctuations the general relaxation equation of Huber is r ecovered, which includes the stretched exponential equation as a parti cular case, whereas for intermittent fluctuations a more complicated u niversal relaxation equation is obtained which includes Huber's equati on, the stretched exponential, and the inverse power law relaxation eq uations as particular cases. [S1063-651X(96)07805-1]