4 LowTemperature Entropy (Alleged Third Law)
As mentioned in the introduction, one sometimes hears the assertion
that the entropy of a system must go to zero as the temperature goes
to zero.
There is no theoretical basis for this assertion, so far as I know –
just unsubstantiated opinion.
As for experimental evidence, I know of only one case where (if I work
hard enough) I can make this statement true, while there are
innumerable cases where it is not true:

There is such a thing as a spin glass. It is a solid,
with a spin at every site. At low temperatures, these spins are not
lined up; they are highly disordered. And there is a large potential
barrier that prevents the spins from flipping. So for all practical
purposes, the entropy of these spins is frozen in. The molar entropy
involved is substantial, on the order of one J/K/mole. You can
calculate the amount of entropy based on measurements of the magnetic
properties.
 A chunk of ordinary glass (e.g. window glass) has a
considerable amount of frozenin entropy, due to the disorderly
spatial arrangement of the glass molecules. That is, glass is not a
perfect crystal. Again, the molar entropy is quite substantial. It
can be measured by Xray scattering and neutron scattering
experiments.
 For that matter, it is proverbial that perfect crystals do not
occur in nature. This is because it is energetically more favorable
for a crystal to grow at a dislocation. Furthermore, the materials
from which the crystal was grown will have chemical impurities, not
to mention a mixture of isotopes. So any real crystal will have
frozenin nonuniformities. The molar entropy might be rather less
than one J/K/mole, but it won’t be zero.
 If I wanted to create a sample where the entropy went to zero
in the limit of zero temperature, I would proceed as follows: Start
with a sample of helium. Cool it to some very low temperature. The
superfluid fraction is a single quantum state, so it has zero
entropy. But the sample as a whole still has nonzero entropy,
because ^{3}He is quite soluble in ^{4}He (about 6% at
zero temperature), and there will
always be some ^{3}He around. To get rid of that, pump the sample
through a superleak, so the ^{3}He is left behind. (Call it reverse
osmosis if you like.) Repeat this as a function of T. As T goes
to zero, the superfluid fraction goes to 100% (i.e. the normalfluid
fraction goes to 0%) so the entropy, as far as I know, would go to
zero asymptotically.
Note: It is hard to measure the lowtemperature entropy by means of
elementary thermal measurements, because typically such measurements
are insensitive to “spectator entropy” as discussed in
section 12.6. So for typical classical thermodynamic
purposes, it doesn’t matter whether the entropy goes to zero or not.