In several recent publications Carlip, as well as Balachandran, Chanda
r, and Momen, has proposed a statistical-mechanical interpretation for
black hole entropy in terms of ''would-be gauge'' degrees of freedom
that become dynamical on the boundary to spacetime. After critically d
iscussing several routes for deriving a boundary action, we examine th
eir hypothesis in the context of generic 2D dilaton gravity. We first
calculate the corresponding statistical-mechanical entropy of black ho
les in 1+1 de Sitter gravity, which has a gauge theory formulation as
a BF theory. Then we generalize the method to dilaton gravity theories
that do not have a (standard) gauge theory formulation. This is facil
itated greatly by the Poisson sigma-model formulation of these theorie
s. It turns out that the phase space of the boundary particles coincid
es precisely with a symplectic leaf of the Poisson manifold that enter
s as target space of the sigma model. Despite this qualitatively appea
ling picture, the quantitative results are discouraging: In most of th
e cases, the symplectic leaves are noncompact and the number of micros
tates yields a meaningless infinity. In those cases where the particle
phase space is compact-such as, e.g., in the Euclidean de Sitter theo
ry-the edge state degeneracy is finite, but generically it is far too
small to account for the semiclassical Bekenstein-Hawking entropy.