  This theoretical paper is to advance a phenomenological, quasi thermodynamic
approach to the dynamics of classical liquids which uses the Levy distribution
of probability theory. Doubts from the chemical physics community about the
application of its unusual properties to this field are tried to be removed. In
particular, to understand the preponderant component of the Levy sum for Glarum
Levy defects and Fischer speckles, the classical mathematical proof [D. A.
Darling, Trans. Amer. Math. Soc. 73, 95 (1952)] for the existence and the
influence of this component is accompanied by addition of physical arguments
related to these defects. It is tried to explain an underlying fluctuating
spatial pattern of free volume with weak contrast and a pattern of mobility
with strong contrast, and to explain the characteristic lengths for the main
transition and the Fischer modes. The structure of the relaxation chart
(dynamic glass transition) and several properties of, and relations between,
the slower dispersion zones therein, are reviewed for classical glassforming
liquids of moderate complexity. For the main transition, the preponderant
component is pushed in the midst of the defect and induces the molecule to its
diffusion step across the cage door of the next neighbors. An Experimentum
Crucis for an indirect proof of the existence of defects - via characteristic
lengths - is also described.
