  The excess entropy, Se, defined as the difference between the entropies of
the liquid and the ideal gas under identical density and temperature
conditions, is shown to be the critical quantity connecting the structural,
diffusional and density anomalies in water-like liquids. Based on simulations
of silica and the two-scale ramp liquids, water-like density and diffusional
anomalies can be seen as consequences of a characteristic non-monotonic density
dependence of Se. The relationship between excess entropy, the order metrics
and the structural anomaly can be understood using a pair correlation
approximation to Se.
