On Page's examples challenging the entropy bound

Abstract

According to the entropy bound, the entropy of a complete physical system can be universally bounded in terms of its circumscribing radius and total gravitating energy. Page's three recent candidates for counterexamples to the bound are here clarified and refuted by stressing that the energies of all essential parts of the system must be included in the energy the bound speaks about. Additionally, in response to an oft heard claim revived by Page, I give a short argument showing why the entropy bound is obeyed at low temperatures by a complete system. Finally, I remark that Page's renewed appeal to the venerable ``many species'' argument against the entropy bound seems to be inconsistent with quantum field theory.