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.
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