  Interior models of Uranus and Neptune often assume discrete layers, but sharp
interfaces are expected only if major constituents are immiscible. Diffuse
interfaces could arise if accretion favored a central concentration of the
least volatile constituents (also incidentally the most dense); compositional
gradients arising in such a structure would likely inhibit convection.
Currently, two lines of evidence suggest possible hydrogen-water immiscibility
in ice giant interiors. The first arises from crude extrapolation of the
experimental hydrogen-water critical curve to $\sim 3$ GPa (Bali et al. 2013).
The data are obtained for an impure system containing silicates, though Uranus
and Neptune could also be "dirty." Current ab initio models disagree (Soubiran
& Militzer 2015), though hydrogen and water are difficult to model from
first-principles quantum mechanics with the necessary precision. The second
argument for hydrogen-water immiscibility in ice giants, outlined herein,
invokes reasoning about the gravitational and magnetic fields. While consensus
remains lacking, here we examine the immiscible case. Applying the resulting
thermodynamic constraints, we find that Neptune models with envelopes
containing a substantial water mole fraction, as much as $\chi \gtrsim 0.1$
relative to hydrogen, can satisfy observations. In contrast, Uranus models
appear to require $\chi \lesssim 0.01$, potentially suggestive of fully demixed
hydrogen and water. Enough gravitational potential energy would be available
from gradual hydrogen-water demixing, to supply Neptune's present-day heatflow
for roughly ten solar system lifetimes. Hydrogen-water demixing could slow
Neptune's cooling rate by an order of magnitude; different hydrogen-water
demixing states could account for the different heatflows of Uranus and
Neptune.
