Water is thought to be a major constituent of celestial bodies formed far enough from their host star for H2O to condense. The transport properties of water at extreme pT-conditions govern the evolution of water-rich planets and moons, such as the ice giants (Uranus and Neptune), or satellites possessing rigid icy shells and interior water oceans, like Europa and Enceladus. New theoretical and data-analysis methods have been recently developed to estimate accurate transport coefficients of electronically-gapped materials from ab initio equilibrium molecular dynamics and the Green-Kubo theory of linear response [1-3]. In this talk, we report on recent results on the application of these methods to heat and charge transport in water at the extreme pT-conditions occurring in the interior of water-rich planets and moons, in all the different relevant phases (partially dissociated liquid, solid, and super-ionic) .
These results are finally employed to build a model of the thermal evolution of Uranus, which accounts for its hitherto poorly understood very low luminosity .
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 F. Grasselli and S. Baroni, Nature Physics 15, 967–972 (2019)
 R. Bertossa, F. Grasselli, L. Ercole, and S. Baroni, Phys. Rev. Lett. 122, 255901 (2019)
 F. Grasselli, L. Stixrude, S. Baroni, arXiv:2003.12557 [cond-mat.mtrl-sci] (2020)
 L. Stixrude, S. Baroni, F. Grasselli, in preparation.