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Statistical Mechanics of the Anomalous Behavior of Tetrahedral Liquids

Tetrahedral liquids such as water and silica-melt show unusual thermodynamic behavior such as a density maximum and an increase in specific-heat when cooled to low temperatures. There is a debate in the literature whether these phenomena stem from a phase transition into a low-density and high-density liquid phases, which occur in the supercooled regime. Here we consider a model of tetrahedral liquids for which we construct a volume-constrained statistical mechanical theory which quantifies the local structure of the liquid. We compare the theory to molecular dynamics simulations and show that the theory can rationalize the simulations semi-quantitatively. We show that the anomalous density and specific heat behavior arise naturally from this theory without exhibiting a liquid-liquid phase-transition. We explain that this theory may or may not have a phase transition, depending on the volume and temperature dependence of the energy and entropy which are sensitive to small changes in the parameters of the model.