  We present results from ab initio simulations of liquid water-hydrogen
mixtures in the range from 2 to 70 GPa and from 1000 to 6000 K, covering
conditions in the interiors of ice giant planets and parts of the outer
envelope of gas giant planets. In addition to computing the pressure and the
internal energy, we derive the Gibbs free energy by performing a thermodynamic
integration. For all conditions under consideration, our simulations predict
hydrogen and water to mix in all proportions. The thermodynamic behavior of the
mixture can be well described with an ideal mixing approximation. We suggest a
substantial fraction of water and hydrogen in giant planets may occur in
homogeneously mixed form rather than in separate layers. The extend of mixing
depends on the planet's interior dynamics and its conditions of formation, in
particular on how much hydrogen was present when icy planetesimals were
delivered. Based on our results, we do not predict water-hydrogen mixtures to
phase separate during any stage of the evolution of giant planets. We also show
that the hydrogen content of an exoplanet is much higher if the mixed interior
is assumed.
