The microscopic structural origin of water's anomalies*

Water displays a vast array of unique properties, known as water's anomalies, whose origin remains subject to hot debate. It's now widely believed that the thermodynamic and dynamic anomalies have different origins, criticality associated with the Widom line and glass transition respectively. Contrary to this dual explanation, here we provide the first unified microscopic physical picture of the water's anomalies in terms of locally favored structures. This common structural origin has a hierarchical impact on the anomalies, where thermodynamic and dynamic ones are affected by the underlying structure only at different length scales. Thermodynamic anomalies are described by a microscopic order parameter, which is the translational order of the second shell, while dynamic ones by the same order parameter after spatial coarse-graining up to neighbors, since the dynamics of a molecule is not determined locally but under the influence of its nearest-neighbor environment. To incorporate this, we develop a novel hierarchical two-state model. We show by extensive simulations of two popular water models that both thermodynamic and kinetic anomalies can be almost perfectly explained by the temperature and pressure dependence of these static and dynamic order parameters respectively.