Scaling law for the glass and Ferry temperatures in the Gaussian random energy model

The Gaussian random energy model (REM) implies a non-Arrhenius temperature dependence for the characteristic relaxation time in the high-viscosity (supercooled) regime of glass-forming liquids. For example, the temperature dependence of the viscosity of the supercooled liquid is given as η(T)≊η0 exp[(TF/T)2]. TF is denoted as the Ferry temperature. The REM exhibits a (glass) transition at a temperature Tg. The REM predicts a scaling law for the two characteristic temperatures, TF=α(log ℜ)1/2Tg where N is the total number of energy levels of the system and α≊1. The scaling law has been successfully applied to a large number of glass-forming liquids as well as biopolymers.