Mass of the system depends both on the enthalpy and the Gibbs free energy but not on the Helmholtz free energy.

That is surprising to me. Helmholtz free energy assumes constant volume (while Gibbs assumes constant pressure). Since we know that pressure is a component of the energy of a system, wouldn't it be more reasonable to use Helmholtz than Gibbs?

Also, if the free energy DOES enter into the considerations, then we have to be careful about the temperature/mass relationship--there are a number of systems for which the free energy decreases as temperature increases. Also if there is a significant contribution from entropic terms, this would further complicate the nature of black holes (if they weren't already problematic).

If we imagine a "planet-sized" sphere of liquid composed of two perfectly miscible isomeric liquids (for the sake of argument, let's say that they have identical densities and identical intermolecular interactions), let's call them A and isoA. If the two liquids are segregated into opposite hemispheres and then allowed to mix (because of my assumptions, ΔU = 0 for this process), are you predicting the total mass of the sphere would decrease?