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The temperature-dependent changes of molecular and sub-molecular motions are studied in amorphous substances. The solid and liquid phases of amorphous bodies are characterized at the micro-level by two types of oscillators, linear and non-linear. It is accepted that an amorphous liquid is formed by domains that group the linear oscillators into the form of icebergs. The serial connection of the viscoelastic elements are arranged inside of these icebergs. The size of the linear connection within the domains is characterized by the number “n”, which increases during the cooling process. The linear viscoelastic behavior of the individual serial connections is connected to the individual relaxation processes α, β, and γ. Only the “alpha” process exhibits growth of “n” to infinity on cooling. Therefore, the corresponding relaxation time, τα, for the infinite chain of “n” elements (Voigt or Maxwell elements) can also reach infinity as the material transforms to a glassy state. In contrast to the “alpha” process, the β and γ processes are limited in growth for serial connections in a chain structure. Therefore, the relaxation times for the β and γ processes, τβ and τγ, will only follow the temperature dependence of the sample viscosity on cooling, which is, of course, Arrhenian. We discuss the role of non-linear oscillators in the solid-liquid transition in relation to Brownian motion

Arrhenian and Non-Arrhenian Temperature Dependent Relaxation Time Development in the Solid-Liquid Transition Area of Amorphous Bodies