  Using a general model for the equilibrium dynamics of supercooled liquids, I
compute from molecular properties the emergent length and time scales that
govern the nonequilibrium relaxation behavior of amorphous ice prepared by
rapid cooling. Upon cooling, the liquid water falls out of equilibrium whereby
the temperature dependence of its relaxation time is predicted to change from
super-Arrhenius to Arrhenius. A consequence of this crossover is that the
location of the apparent glass transition temperature depends logarithmically
on cooling rate. Accompanying vitrification is the emergence of a dynamical
length-scale, the size of which depends on the cooling rate and varies between
angstroms and 10s of nanometers. While this protocol dependence clarifies a
number of previous experimental observations for amorphous ice, the arguments
are general and can be extended to other glass forming liquids.
