  We calculate the Casimir energy and entropy for two perfect metal spheres in
the large and short separation limit. We obtain nonmonotonic behavior of the
Helmholtz free energy with separation and temperature, leading to parameter
ranges with negative entropy, and also nonmonotonic behavior of the entropy
with temperature and with the separation between the spheres. The appearance of
this anomalous behavior of the entropy is discussed as well as its
thermodynamic consequences.
