It has been suggested recently that the microcanonical entropy of a system
may be accurately reproduced by including a logarithmic correction to the
canonical entropy. In this paper we test this claim both analytically and
numerically by considering three simple thermodynamic models whose energy
spectrum may be defined in terms of one quantum number only, as in a
non-rotating black hole. The first two pertain to collections of noninteracting
bosons, with logarithmic and power-law spectra. The last is an area ensemble
for a black hole with equi-spaced area spectrum. In this case, the many-body
degeneracy factor can be obtained analytically in a closed form. We also show
that in this model, the leading term in the entropy is proportional to the
horizon area A, and the next term is ln A with a negative coefficient.Comment: 15 pages, 1 figur