  It is shown that, for systems in which the entropy is an extensive function
of the energy and volume, the Bekenstein and the holographic entropy bounds
predict new results. More explicitly, the Bekenstein entropy bound leads to the
entropy of thermal radiation (the Unruh-Wald bound) and the spherical entropy
bound implies the "causal entropy bound". Surprisingly, the first bound shows a
close relationship between black hole physics and the Stephan-Boltzmann law
(for the energy and entropy flux densities of the radiation emitted by a hot
blackbody). Furthermore, we find that the number of different species of
massless fields is bounded by $\sim 10^{4}$.
