  We calculate the Casimir energy and entropy for two spheres described by the
perfect metal model, plasma model, and Drude model in the large separation
limit. We obtain nonmonotonic behavior of the Helmholtz free energy with
separation and temperature for the perfect metal and plasma models, leading to
parameter ranges with negative entropy, and also nonmonotonic behavior of the
entropy with temperature and the separation between the spheres. This
nonmonotonic behavior has not been found for Drude model. The appearance of
this anomalous behavior of the entropy is discussed as well as its
thermodynamic consequences.
