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