We use molecular dynamics computer simulations to evaluate the thermodynami
c properties of deeply supercooled liquid water. We find strong evidence th
at the experimentally observed polyamorphism of amorphous solid water is th
e manifestation, for temperatures below the glass transition, of equilibriu
m thermodynamic properties of the Liquid. Specifically, the simulation data
predict that a line of maxima of the isothermal compressibility occurs in
Liquid water and that polyamorphism is a consequence of the influence of th
is maximum on the mechanical behavior of the amorphous solid. We also find
evidence that the compressibility maximum may develop as temperature decrea
ses into a critical point and line of liquid-liquid phase transitions. We s
how that such a novel phase transition is consistent with the anomalous the
rmodynamic properties of the liquid, and also elucidates the kinetics of cr
ystal nucleation in supercooled water.