Radiation entropy bound from the second law of thermodynamics

It has been suggested heuristically by Unruh and Wald, and independently by Page, that among systems with given energy and volume, thermal radiation has the largest entropy. The suggestion leads to the corresponding universal bound on entropy of physical systems. Using a gedanken experiment we show that the bound follows from the second law of thermodynamics if the CPT symmetry is assumed and a certain general condition on matter holds. The experiment suggests that a wide class of Lorentz invariant local quantum field theories obeys a bound on the density of states.