The Adam-Gibbs (AG) expression linking relaxation times with configurational entropy gives a good account of the non-linearity observed in enthalpy relaxation of amorphous polymeric, inorganic, and simple molecular materials near and below T(g). Data analyses yield zero-entropy temperatures that are comparable with available Kauzmann values. The AG formulation, when coupled with a few plausible ancillary assumptions, predicts correlations between the Arrhenius parameters x, DELTA-h*, and the KWW exponent beta that are observed experimentally. It is suggested that the AG primary activation energy, DELTA-mu, is the single causative factor that generates these correlations.