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This theoretical paper is to advance a phenomenological, quasi thermodynamicapproach to the dynamics of classical liquids which uses the Levy distributionof probability theory. Doubts from the chemical physics community about theapplication of its unusual properties to this field are tried to be removed. Inparticular, to understand the preponderant component of the Levy sum for GlarumLevy defects and Fischer speckles, the classical mathematical proof [D. A.Darling, Trans. Amer. Math. Soc. 73, 95 (1952)] for the existence and theinfluence of this component is accompanied by addition of physical argumentsrelated to these defects. It is tried to explain an underlying fluctuatingspatial pattern of free volume with weak contrast and a pattern of mobilitywith strong contrast, and to explain the characteristic lengths for the maintransition 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 glassformingliquids of moderate complexity. For the main transition, the preponderantcomponent is pushed in the midst of the defect and induces the molecule to itsdiffusion step across the cage door of the next neighbors. An ExperimentumCrucis for an indirect proof of the existence of defects - via characteristiclengths - is also described.

Levy defects in fluctuating pattern of liquids. A quasi thermodynamic approach to the dynamic glass transition in classical molecular liquids