"Will you now admit that a molecule of Ice atop Mt Everest has lower entropy and higher potential energy than a molecule of water in the Indian Ocean? Yes or No?""
"Oh yes, Mr. Bill. Ice always has a lower entropy and lower [heat] energy level than water."
Dear Mr. Bill. A lower entropy and a higher potential energy are the same thing. When I say ice has a lower entropy, it is equal to your claim that ice has a higher potential energy. It's not that ice has a lower entropy *and* a higher potential energy. You are only describing one attribute of ice using two different terms. IOW, they are two different ways of describing the same thing.
I was talking about 2 different things. A lower entropy (or higher potential energy for you) and a lower heat energy due to the loss of the latent heat of freezing. Ice gives up huge quantities of heat energy when it freezes as the 'latent heat of freezing'. This means that ice will always have a lower heat energy than water, which is what I said. Your insistence that lower entropy equals higher potential energy is fine. You can define lower entropy as higher potential energy and it doesn't change what I said.
If restate my statement using your terms, my quote would read...
"Oh yes, Mr. Bill. Ice always has a higher potential energy and lower heat energy level than water."
I think maybe you are confused because entropy goes from lower entropy to higher entropy while potential energy goes from higher to lower, assuming you are describing the same system moving in the same direction in accordance w/ the laws of thermodynamics. They are simply two different ways of describing the 'direction' of one attribute of a system as it relates to entropy or 'potential energy'.
Are you confused because you think my reference to lower heat energy means a lower potential energy? Is that it? I thought I had explained that sufficiently, but apparently not. Hopefully now you understand.