We develop a self-consistent thermodynamic description of silicate liquids applicable across the entire mantle pressure and temperature regime. The description combines the finite strain free energy expansion with an account of the temperature dependence of liquid properties into a single fundamental relation, while honouring the expected limiting behaviour at large volume and high temperature. We find that the fundamental relation describes well previous experimental and theoretical results for liquid MgO, MgSiO 3 , Mg 2 SiO 4 and SiO 2 . We apply the description to calculate melting curves and Hugoniots of solid and liquid MgO and MgSiO 3 . For periclase, we find a melting temperature at the core–mantle boundary (CMB) of 7810 ± 160 K , with the solid Hugoniot crossing the melting curve at 375 GPa, 9580 K , and the liquid Hugoniot crossing at 470 GPa, 9870 K . For complete shock melting of periclase we predict a density increase of 0.14 g cm −3 and a sound speed decrease of 2.2 km s −1 . For perovskite, we find a melting temperature at the CMB of 5100 ± 100 K with the perovskite section of the enstatite Hugoniot crossing the melting curve at 150 GPa, 5190 K , and the liquid Hugoniot crossing at 220 GPa, 5520 K . For complete shock melting of perovskite along the enstatite principal Hugoniot, we predict a density increase of 0.10 g cm −3 , with a sound speed decrease of 2.6 km s −1
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