  We investigate the large-scale structure of amorphous ices and transitions
between their different forms by quantifying their large-scale density
fluctuations. Specifically, we simulate the isothermal compression of
low-density amorphous ice (LDA) and hexagonal ice (Ih) to produce high-density
amorphous ice (HDA). Remarkably, both HDA and LDA are nearly hyperuniform,
meaning that they are characterized by an anomalous suppression of large-scale
density fluctuations. By contrast, in correspondence with both non-equilibrium
phase transitions to HDA, the presence of structural heterogeneities strongly
suppresses the hyperuniformity and, remarkably, the system becomes
hyposurficial (devoid of "surface-area" fluctuations). Our investigation
challenges the largely accepted "frozen-liquid" picture, which views glasses as
structurally arrested liquids. Beyond implications for water, our findings
enrich our understanding of the structural transformations that occur in
glasses with varying pressures.
