  We explore the validity of the generalized Bekenstein bound, S <= pi M a. We
define the entropy S as the logarithm of the number of states which have energy
eigenvalue below M and are localized to a flat space region of width a. If
boundary conditions that localize field modes are imposed by fiat, then the
bound encounters well-known difficulties with negative Casimir energy and large
species number, as well as novel problems arising only in the generalized form.
In realistic systems, however, finite-size effects contribute additional
energy. We study two different models for estimating such contributions. Our
analysis suggests that the bound is both valid and nontrivial if interactions
are properly included, so that the entropy S counts the bound states of
interacting fields.
