  Deeply supercooled water exhibits complex dynamics with large density
fluctuations, ice coarsening and characteristic time scales extending from
picoseconds to milliseconds. Here, we discuss implications of these time scales
as they pertain to two-phase coexistence and to molecular simulations of
supercooled water. Specifically, we argue that it is possible to discount
liquid-liquid criticality because the time scales imply that correlation
lengths for such behavior would be bounded by no more than a few nanometers.
Similarly, it is possible to discount two-liquid coexistence because the time
scales imply a bounded interfacial free energy that cannot grow in proportion
to a macroscopic surface area. From time scales alone, therefore, we see that
coexisting domains of differing density in supercooled water can be no more
than nano-scale transient fluctuations.
