  The Bousso entropy bound, in its generalized form, is investigated for the
case of perfect fluids at local thermodynamic equilibrium and evidence is found
that the bound is satisfied if and only if a certain local thermodynamic
property holds, emerging when the attempt is made to apply the bound to thin
layers of matter. This property consists in the existence of an ultimate lower
limit l* to the thickness of the slices for which a statistical-mechanical
description is viable, depending l* on the thermodynamical variables which
define the state of the system locally. This limiting scale, found to be in
general much larger than the Planck scale (so that no Planck scale physics must
be necessarily invoked to justify it), appears not related to gravity and this
suggests that the generalized entropy bound is likely to be rooted on
conventional flat-spacetime statistical mechanics, with the maximum admitted
entropy being however actually determined also by gravity.
  Some examples of ideal fluids are considered in order to identify the
mechanisms which can set a lower limit to the statistical-mechanical
description and these systems are found to respect the lower limiting scale l*.
The photon gas, in particular, appears to seemingly saturate this limiting
scale and the consequence is drawn that for systems consisting of a single
slice of a photon gas with thickness l*, the generalized Bousso bound is
saturated. It is argued that this seems to open the way to a peculiar
understanding of black hole entropy: if an entropy can meaningfully (i.e. with
a second law) be assigned to a black hole, the value A/4 for it (where A is the
area of the black hole) is required simply by (conventional) statistical
mechanics coupled to general relativity.
