In the high and low temperature limits, viscous flow in amorphous materials (e.g. in glasses and melts) has the Arrhenius form:
where  is a relevant activation energy, given in terms of molecular parameters;  is temperature;  is the molar gas constant; and  is approximately a constant. The activation energy  takes a different value depending on whether the high or low temperature limit is being considered: it changes from a high value  at low temperatures (in the glassy state) to a low value  at high temperatures (in the liquid state).
For intermediate temperatures,  varies nontrivially with temperature and the simple Arrhenius form fails. On the other hand, the two-exponential equation
where , , ,  are all constants, provides a good fit to experimental data over the entire range of temperatures, while at the same time reducing to the correct Arrhenius form in the low and high temperature limits. This expression can be motivated from various theoretical models of amorphous materials at the atomic level.
A two-exponential equation for the viscosity can be derived within the Dyre shoving model of supercooled liquids, where the Arrhenius energy barrier is identified with the high-frequency shear modulus times a characteristic shoving volume. Upon specifying the temperature dependence of the shear modulus via thermal expansion and via the repulsive part of the intermolecular potential, another two-exponential equation is retrieved:
where  denotes the high-frequency shear modulus of the material evaluated at a temperature equal to the glass transition temperature ,  is the so-called shoving volume, i.e. it is the characteristic volume of the group of atoms involved in the shoving event by which an atom/molecule escapes from the cage of nearest-neighbours, typically on the order of the volume occupied by few atoms. Furthermore,  is the thermal expansion coefficient of the material,  is a parameter which measures the steepness of the power-law rise of the ascending flank of the first peak of the radial distribution function, and is quantitatively related to the repulsive part of the interatomic potential. Finally,  denotes the Boltzmann constant.