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At zero temperature, the entropy of generic systems need not vanish, but often seems to in practice. I would like to know some concrete examples where $S\neq 0$ at $T=0$.

A very high-energy flavored scenario where $S\neq 0$ at $T=0$ is the case of extremal black holes, where $S=\frac{\rm Area}{4G_N}\neq 0$. I believe glassy systems (and frustrated systems, more generally) also have non-trivial zero-$T$ entropy.

What are some additional systems which have $S\neq 0$ at $T=0$? References are appreciated.

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According to the third law of thermodynamics, any system approaching 0 Kelvin approaches a constant value of entropy. Crystalline systems approach zero entropy state, while amorphous systems do not reach a state of 0 entropy, rather just a state of constant entropy.

Most solids would be classified under amorphous, and hence we can say most will not have zero entropy at 0 K. Glasses and gels are some examples

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