Anomalous diffusion producing normal relaxation and transport

From the Arrhenius law a probability distribution of timescales is derived by treating both the prefactor and the activation energy as random variables. In the defect-diffusion model this probability distribution is used to calculate the properties of the anomalous diffusion of defects. The timescales represent the pausing time distribution between movements of a defect. The conditions are determined for these mobile defects to produce stretched exponential relaxation. The diffusion of a single defect is anomalous, but the collective effect of all defects produces a characteristic relaxation timescale. The temperature and pressure dependence of this timescale is used to determine conductivity, dielectric relaxation, and viscosity