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Correct statements about samples of ice and liquid water at 0 degrees Celsius include which of the following?

I. Molecules in ice and liquid water have the same KE
II. Liquid water has a greater entropy than ice/
III. Liquid water has a greater potential energy than ice.

Apparently, all I, II, III are right. I thought at 0 degrees, both phases are at equilibrium so entropy is equal on both sides. Also, shouldn't PE=KE at equilibrium?