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An important extensive property of all systems in thermodynamics, statistical mechanics, and information theory, quantifying their disorder (randomness), i.e., our lack of information about them. It characterizes the degree to which the energy of the system is *not* available to do useful work.

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Why the entropy of non-zero nuclear spin is zero at $T = 0$?

We are told by the third law that its entropy is zero. However, let us further suppose that each atom has at its centre a nucleus with angular momentum quantum number $I$. … How can we reconcile this with zero entropy since the non-zero nuclear spin implies that the entropy $S$ of this system should be $S= Nk\ln(2I + 1)$,to however low a temperature we cool it? …
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