We
develop a simple yet comprehensive nonlinear model to describe
relaxation phenomena in amorphous glass-formers near the glass transition
temperature. The model is based on the two-state, two-(time)scale
(TS2) framework and describes the isothermal relaxation of specific
volume, enthalpy, or shear stress via a simple first-order nonlinear
differential equation (the Trachenko-Zaccone [TZ] equation) for local
cooperative events. These nonlinear dynamics of cooperatively rearranging
regions naturally arise from the TS2 framework. We demonstrate that
the solutions of the TZ equation comprehensively encompass the Debye
exponential relaxation, the Kohlrausch–Williams–Watts
stretched and compressed relaxations, and the Guiu–Pratt logarithmic
relaxation. Furthermore, for the case of stress relaxation modeling,
our model recovers, as one of its limits, the Eyring law for plastic
flow, where the Eyring activation volume is related to thermodynamic
parameters of the material. Using the example of polystyrene, we demonstrate
how our model successfully describes the Kovacs’ “asymmetry
of approach” specific volume and enthalpy experiments, as well
as the stress relaxation. Other potential applications of the model,
including the dielectric relaxation, are also discussed. The presented
approach disentangles the physical origins of different relaxation
laws within a single general framework based on the underlying physics.