  The generalized covariant entropy bound is the conjecture that the entropy of
the matter present on any non-expanding null hypersurface L will not exceed the
difference between the areas, in Planck units, of the initial and final spatial
2-surfaces bounding L. The generalized Bekenstein bound is a special case which
states that the entropy of a weakly gravitating isolated matter system will not
exceed the product of its mass and its width. Here we show that both bounds can
be derived directly from the following phenomenological assumptions: that
entropy can be computed by integrating an entropy current which vanishes on the
initial boundary and whose gradient is bounded by the energy density. Though we
note that any local description of entropy has intrinsic limitations, we argue
that our assumptions apply in a wide regime. We closely follow the framework of
an earlier derivation, but our assumptions take a simpler form, making their
validity more transparent in some examples.
