The Boulware State and the Generalised Second Law of Thermodynamics

We show that the appropriate vacuum state for the interior of a box with reflecting walls being lowered adiabatically into a Schwarzschild black hole is the Boulware state. This is concordant with the results of Unruh and Wald, who used a different approach to obtain the stress-energy inside the box. Some comments about an entropy bound for ordinary matter, as first conjectured by Bekenstein, are presented.