The ideal quantum gases satisfying Bose-Einstein statistics in d dimensions (d=1,2,3,. . .) provide illuminating apparent counterexamples to the often-supposed equivalence of the Nernst-Simon and unattainability statements of the third law of thermodynamics. These gases satisfy the second law of thermodynamics and the Nernst-Simon and Planck statements of the third law but appear to violate, at least in a technical sense, the unattainability statement. They do so by virtue of the fact that their entropy vanishes at nonzero temperature and bounded pressure. Possible objections to the counterexamples are examined and additional counterexamples are produced with the same mechanism. An interpretation of this nonequivalence is proposed in terms of a statement about the kinds of Hamiltonians found in nature.

• Received 4 January 1991

DOI:https://doi.org/10.1103/PhysRevA.43.5289