  Recent computational studies have reported evidence of a metastable
liquid-liquid phase transition (LLPT) in molecular models of water under deeply
supercooled conditions. A competing hypothesis suggests, however, that
non-equilibrium artifacts associated with coarsening of the stable crystal
phase have been mistaken for an LLPT in these models. Such artifacts are
posited to arise due to a separation of time scales in which density
fluctuations in the supercooled liquid relax orders of magnitude faster than
those associated with bond-orientational order. Here, we use molecular
simulation to investigate the relaxation of density and bond-orientational
fluctuations in three molecular models of water (ST2, TIP5P and TIP4P/2005) in
the vicinity of their reported LLPT. For each model, we find that density is
the slowly relaxing variable under such conditions. We also observe similar
behavior in the coarse-grained mW model of water. Our findings therefore
challenge the key physical assumption underlying the competing hypothesis.e
find that density relaxes significantly faster than bond-orientational order,
as incorrectly predicted by this competing hypothesis.
