Acceleration radiation and the generalized second law of thermodynamics

It is shown that the Bekenstein limit, $\frac{S}{E}\le 2\pi R$, for the entropy-to-energy ratio of matter confined by a box of size $R$ is not needed for the validity of the generalized second law of thermodynamics. If one attempts to slowly lower a box containing rest energy $E$ and entropy $S$ into a black hole, there will be an effective buoyancy force on the box caused by the acceleration radiation felt by the box when it is suspended near the black hole. As a result there is a finite lower bound on the energy delivered to the black hole in this process and thus a minimal area increase which turns out to be just sufficient to ensure that the generalized second law of thermodynamics is satisfied. By reversing this process, we can "mine" energy from a black hole. The nature of these processes is also analyzed from an inertial point of view, and the mechanism by which energy is transported into and out of the black hole is explained. Analogous effects for accelerating boxes in flat spacetime are also analyzed.