Statistical Mechanics and Dynamics of a Three-Dimensional Glass-Forming System

In the context of a classical example of glass formation in three dimensions, we exemplify how to construct a statistical-mechanical theory of the glass transition. At the heart of the approach is a simple criterion for verifying a proper choice of upscaled quasispecies that allow the construction of a theory with a finite number of “states.” Once constructed, the theory identifies a typical scale ξ that increases rapidly with lowering the temperature and which determines the α-relaxation time τ_α as τ_α∼exp⁡(μξ/T), with μ a typical chemical potential. The theory can predict relaxation times at temperatures that are inaccessible to numerical simulations.