The Nernst formulation of the third law of ordinary thermodynamics (often
referred to as the ``Nernst theorem'') asserts that the entropy, S, of a
system must go to zero (or a ``universal constant'') as its temperature, T,
goes to zero. This assertion is commonly considered to be a fundamental law of
thermodynamics. As such, it seems to spoil the otherwise perfect analogy
between the ordinary laws of thermodynamics and the laws of black hole
mechanics, since rotating black holes in general relativity do not satisfy the
analog of the ``Nernst theorem''. The main purpose of this paper is to attempt
to lay to rest the ``Nernst theorem'' as a law of thermodynamics. We consider a
boson (or fermion) ideal gas with its total angular momentum, J, as an
additional state parameter, and we analyze the conditions on the single
particle density of states, g(ϵ,j), needed for the Nernst formulation
of the third law to hold. (Here, ϵ and j denote the single particle
energy and angular momentum.) Although it is shown that the Nernst formulation
of the third law does indeed hold under a wide range of conditions, some simple
classes of examples of densities of states which violate the ``Nernst theorem''
are given. In particular, at zero temperature, a boson (or fermion) gas
confined to a circular string (whose energy is proportional to its length) not
only violates the ``Nernst theorem'' also but reproduces some other
thermodynamic properties of an extremal rotating black hole.Comment: 20 pages, plain LaTeX fil