We present new equations of state (EOS) for hydrogen and helium covering a wide range of temperatures from 60 K to 10 7 K and densities from 10 −10 g/cm 3 to 10 3 g/cm 3 . They include an extended set of ab initio EOS data for the strongly correlated quantum regime with an accurate connection to data derived from other approaches for the neighboring regions. We compare linear-mixing isotherms based on our EOS tables with available real-mixture data. A first important astrophysical application of this new EOS data is the calculation of interior models for Jupiter and the comparison with recent results. Secondly, mass-radius relations are calculated for Brown Dwarfs which we compare with predictions derived from the widely used EOS of Saumon, Chabrier and van Horn. Furthermore, we calculate interior models for typical Brown Dwarfs with different masses, namely Corot-3b, Gliese-229b and Corot-15b, and the Giant Planet KOI-889b. The predictions for the central pressures and densities differ by up to 10% dependent on the EOS used. Our EOS tables are made available in the supplemental material of this paper. Subject headings: equation of state -dense matter -plasmas -stars: low-mass, brown dwarfs -planets and satellites: individual(Jupiter)

We use finite-temperature density functional theory coupled to classical molecular dynamics simulation to calculate the miscibility gap of hydrogen-helium mixtures. The van der Waals density functional (vdW-DF) theory is used, which leads to lower demixing temperatures compared to computations using the Perdew-Burke-Ernzerhof functional. Our calculations suggest that current Jupiter models are most likely too hot to allow demixing in the interior. A Jupiter isentrope based on our vdW-DF data is presented. Our demixing phase diagram still predicts phase separation in Saturn, but in a significantly reduced fraction of its volume.

Analytic free energy models for three solid high-pressure phases--diamond, body centered cubic phase with eight atoms in the unit cell (BC8), and simple cubic (SC)--are developed using density functional theory. We explicitly include anharmonic effects by performing molecular dynamics simulations and investigate their density and temperature dependence in detail. Anharmonicity in the nuclear motion shifts the phase transitions significantly compared to the harmonic approximation. Furthermore, we apply a thermodynamically constrained correction that brings the equation of state in accordance with diamond anvil cell experiments. The performance of our thermodynamic functions is validated against Hugoniot experiments.

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We calculate the free energy and other basic thermodynamic properties of water within a model in the chemical picture. The respective mass‐action laws between several molecular, atomic, and ionic species are solved analytically, and purely temperature‐dependent partition functions are used for all species. It is shown that such an ideal gas‐like model is able to describe the thermodynamic properties in relatively good agreement with ab initio simulations, provided that the density of the system is sufficiently low. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)