On the fluctuations that order and frustrate liquid water

At ambient conditions, water sits close to phase coexistence with its crystal. More so than in many other materials, this fact is manifested in the fluctuations that maintain a large degree of local order in the liquid. These fluctuations and how they result in long-ranged order, or its absence, are emergent features of many interacting molecules. Their study therefore requires using the tools of statistical mechanics for their their systematic understanding. In this dissertation we develop such an understanding. In particular, we focus on collective behavior that emerges in liquid and solid water. At room temperatures, the thermophysical properties of water are quantified and rationalized with simple molecular models. A key feature of these models is the correct characterization of the competition between entropic forces of packing and the energetic preference for tetrahedral order. At cold temperatures, the properties of ice surfaces are studied with statistical field theory. The theory we develop for the long wavelength features of ice interfaces allows us to explain the existence of a premelting layer on the surface of ice and the stability of ice in confinement. In between these extremes, the dynamics of supercooled water are considered. A detailed theory for the early stages of coarsening is developed and used to explain the peculiar observation of a transient second liquid state of water. When coarsening dynamics are arrested, the result is the formation of a glassy states of water. We show that out-of-equilibrium the phase diagram for supercooled water exhibits a rich amount of structure, including a triple point between two glass phases of water and the liquid. At the end, we explore possible technological implications for the interplay between ordering and frustration in studies of water at metal interfaces.