  We obtain the asymptotic density of open p-brane states with zero-modes
included. The resulting logarithmic correction to the p-brane entropy has a
coefficient - \frac{p + 2}{2 p}, and is independent of the dimension of the
embedding spacetime. Such logarithmic corrections to the entropy, with
precisely this coefficient, appear in two other contexts also: a gas of
massless particles in p-dimensional space, and a Schwarzschild black hole in (p
+ 2)-dimensional anti de Sitter spacetime.
