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The characterization of the formation mechanisms of amorphous solids is alarge avenue for research, since understanding its non-Arrhenius behavior ischallenging to overcome. In this context, we present one path toward modelingthe diffusive processes in supercooled liquids near glass transition through aclass of non-homogeneous continuity equations, providing a consistenttheoretical basis for the physical interpretation of its non-Arrheniusbehavior. More precisely, we obtain the generalized drag and diffusioncoefficients that allow us to model a wide range of non-Arrhenius processes.This provides a reliable measurement of the degree of fragility of the systemand an estimation of the fragile-to-strong transition in glass-forming liquids,as well as a generalized Stokes-Einstein equation, leading to a betterunderstanding of the classical and quantum effects on the dynamics ofnon-additive stochastic systems.

Characterization of the non-Arrhenius behavior of supercooled liquids by modeling non-additive stochastic systems