The equations governing the small‐signal response of relaxing, nonresonant systems which may be described by a distribution of relaxation times (DRT) and/or a distribution of activation energies (DAE) are summarized and generalized and their implications discussed for several popular distributions. Much past work, both experimental and theoretical, associated with these distributions is discussed. A distinction is made between physically realistic distributions, which involve finite shortest and longest relaxation times, and the usual mathematical approaches which involve limiting zero and infinite relaxation times. The Lévy DRT, which is of the latter character and which leads to the popular stretched exponential (SE) time and Williams–Watts (WW) frequency responses, is inconsistent with a temperature‐independent DAE, reducing its range of applicability for a thermally activated situation. The SE‐WW response has been termed universal; it is not, both because of the above facts and also because it does not lead to the often found symmetrical log‐frequency response. Both Gaussian and exponential DAEs can lead to both symmetrical and skewed results, and can involve either temperature‐dependent or temperature‐independent DAEs. However, the Gaussian DAE does not yield fractional power‐law time or frequency response over a finite, nonzero range, behavior found in nearly all distributed data. However, all DAEs involving exponential probability densities do lead to such behavior and provide, as well, an explanation of the temperature dependence of power‐law exponents. In addition, it appears that the response of systems involving an exponential DAE can fit that of virtually all previous models, including the SE‐WW, and thus can fit all data for thermally activated systems which have been fitted by these models. Problems in data fitting and many sources and types of ambiguity and their resolution are discussed. Special attention is devoted to the distinction between parallel, sequential, and hierarchical microscopic‐model structure and response, and the various different, but, surprisingly, equivalent ways the overall response can be represented mathematically or by means of equivalent circuits of different connectivity.
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