Why is zero entropy possible for a solid at absolute zero temperature? The third law of thermodynamics states that the entropy of a perfect homogeneous solid is zero at absolute zero temperature.
The reason to ask for "perfect and homogeneous" is that such a solid has a ground state that is not degenerate.
But here is the question. A perfect crystal can be oriented in various directions in space. All these orientation are degenerate states. Why are the different states not counted? Shouldn't they lead to a non-zero entropy at absolute zero temperature?
 A: The entropy definition you speak of is based on the numbers of microstates that realise a given macrostate. Now, what exactly is a micro- and macrostate is arbitrary to some extent and mostly changes what question you want your entropy to answer. However, I would argue that at least one of the following applies:

*

*Different orientations of the crystal are different macrostates. Even if your crystal is as perfect a sphere as it can be (and thus a sphere on the macroscopic level), you can distinguish orientations, e.g., with X-ray crystallography. Thus I would consider crystal orientation to be a macroscopic property.


*Different orientations of the crystal are the same microstate. After all, it’s still the very same crystal. This particularly applies if the crystal is floating in a vacuum devoid of external fields such as gravitation and electromagnetism: Here, you cannot distinguish between rotating the crystal and the observer. (See also Themis’ comment.)


*If your crystal is not floating in a vacuum devoid of external fields such as gravitation and electromagnetism, the different rotations are not equivalent anymore. Some orientation of the crystal is gravitationally or electromagnetically favoured and it will turn until it achieves that orientation.
