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Using a general model for the equilibrium dynamics of supercooled liquids, Icompute from molecular properties the emergent length and time scales thatgovern the nonequilibrium relaxation behavior of amorphous ice prepared byrapid cooling. Upon cooling, the liquid water falls out of equilibrium wherebythe temperature dependence of its relaxation time is predicted to change fromsuper-Arrhenius to Arrhenius. A consequence of this crossover is that thelocation of the apparent glass transition temperature depends logarithmicallyon cooling rate. Accompanying vitrification is the emergence of a dynamicallength-scale, the size of which depends on the cooling rate and varies betweenangstroms and 10s of nanometers. While this protocol dependence clarifies anumber of previous experimental observations for amorphous ice, the argumentsare general and can be extended to other glass forming liquids.

The length and time scales of water's glass transitions