  We establish that unitarity of scattering amplitudes imposes universal
entropy bounds. The maximal entropy of a self-sustained quantum field object of
radius R is equal to its surface area and at the same time to the inverse
running coupling evaluated at the scale R. The saturation of these entropy
bounds is in one-to-one correspondence with the non-perturbative saturation of
unitarity by 2-to-N particle scattering amplitudes at the point of optimal
truncation. These bounds are more stringent than Bekenstein's bound and in a
consistent theory all three get saturated simultaneously. This is true for all
known entropy-saturating objects such as solitons, instantons, baryons,
oscillons, black holes or simply lumps of classical fields. We refer to these
collectively as "saturons" and show that in renormalizable theories they behave
in all other respects like black holes. Finally, it is argued that the
confinement in SU(N) gauge theory can be understood as a direct consequence of
the entropy bounds and unitarity.
