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I know the statement "The third law of thermodynamics states that the entropy of a system at absolute zero is a well-defined constant. This is because a system at zero temperature exists in its ground state so that its entropy is determined only by the degeneracy of the ground state."

But I don't yet understand it's a function. I saw in the accepted answer of this post that it plugs a loophole in second law "Is the third law of thermodynamics a non-essential law?" but I don't get what loophole it's fixing.

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