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 $\ensuremath{\xi}$ that increases rapidly with lowering the temperature and which determines the $\ensuremath{\alpha}$-relaxation time ${\ensuremath{\tau}}_{\ensuremath{\alpha}}$ as ${\ensuremath{\tau}}_{\ensuremath{\alpha}}\ensuremath{\sim}\mathrm{exp} (\ensuremath{\mu}\ensuremath{\xi}/T)$, with $\ensuremath{\mu}$ a typical chemical potential. The theory can predict relaxation times at temperatures that are inaccessible to numerical simulations.