So the water loses energy to gravity but at the same time gains exactly the same amount via "thermodynamic gain"? Ok: What is the "thermodynamic gain"? Where does that energy come from?
It comes from the atmosphere, EM radiation, you if you are presence, In my opinion all matter has a sponge like property and can absorb energy or lose energy.
Gravity is a constant force applied, so any object subjective to gravity is always at a loss of its equilibrium to gravity . Gravity is + and minus of energy of mass being attracted to other + and minus of energy of mass. The plus and minus seemingly acting has one force which is gravity. Energy is the only mechanism in any mass that has the force of attraction and repelling, so therefore gravity must be seen has the acting of energies because mass has no other mechanism except energy.
It may surprise you but i am going to explain force, and there is only in my opinion two things associated with force, one being gravity and the second being opposed to gravity, and this is the collective of forces narrowed down to the roots.
P.s Up and down do not exist, only contraction or expanding from the center of mass.
P.s at altitude does water need less energy added to boil?
The Caesium atom ticks faster at altitude because the energy loss to gravity is decreased by distance away from gravity as gravity decreases the clock speeds up because the restriction is removed.
Hopefully by now you can see that it is your science, and I am just re-aligning some aspects and coming up with answers
If you were a Caesium atom and made a Journey to the Sun from the Earth , consider what the effect on the beating of the atom would be, It would firstly speed up in its beats and then has you approached the Sun it would slow back down again , to a slower rate than earth because there is more gravity in the sun, showing you the restriction gravity has on matter.
GPS time delay is a carrier signal entering a medium from a vacuum and in effect slowing down by the refraction of the medium causing a delay and change in velocity from the vacuum speed. The vacuum has no mechanism to propagate an EM wave, where as the medium has an opposing force and resistance to the EM radiation flow
A Neutron star still has gravity because it is either a plus or a minus, and with atoms and matter being of both plus and minus, there is still an attractive force of energy of the mass, so the atoms can be attracted and crushed.
P.s I use the term energy in a broad range because I know science knows the atomic forces etc better than myself.