  In several recent publications Carlip, as well as Balachandran, Chandar and
Momen, have 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 discussing several routes for
deriving a boundary action, we examine their hypothesis in the context of
generic 2-D dilaton gravity. We first calculate the corresponding statistical
mechanical entropy of black holes in 1+1 deSitter 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 facilitated greatly by the Poisson-Sigma-model formulation of these
theories. It turns out that the phase space of the boundary particles coincides
precisely with a symplectic leaf of the Poisson manifold that enters as target
space of the Sigma-model. Despite this qualitatively appealing picture, the
quantitative results are discouraging: In most of the cases the symplectic
leaves are non-compact and the number of microstates yields a meaningless
infinity. In those cases where the particle phase space is compact - such as,
e.g., in the Euclidean deSitter theory - the edge state degeneracy is finite,
but generically it is far too small to account for the semiclassical
Bekenstein-Hawking entropy.
