Title: Thermodynamic Origin of Water's Thermal Conductivity Maximum

Abstract: The thermal conductivity of water features a maximum (TCM) as a function of temperature at constant pressure. By examining why molecular force fields succeed or fail to reproduce the maximum and interpreting our results using the Bridgman equation, we show that water's TCM is connected with its compressibility minimum. Using Stillinger-Weber potentials for tetrahedral liquids, we interpolate between the behaviour of simple liquids and highly tetrahedral materials such as carbon. Together with two vanishing limits at low/high tetrahedrality, we identify three regimes for the TCM: when it originates from either the compressibility minimum or density maximum, or both. Thus, the TCM exists in a "Goldilocks Zone" of tetrahedral order. We provide a thermodynamic explanation for the TCM of not only water, but tetrahedral liquids in general.