Quantum buoyancy, generalized second law, and higher-dimensional entropy bounds

Understand

Bekenstein has presented evidence for the existence of a universal upper bound of magnitude $2\pi R/\hbar c$ to the entropy-to-energy ratio $S/E$ of an arbitrary {\it three} dimensional system of proper radius $R$ and negligible self-gravity.

• In this paper we derive a generalized upper bound on the entropy-to-energy ratio of a $(D+1)$-dimensional system.
• We consider a box full of entropy lowered towards and then dropped into a $(D+1)$-dimensional black hole in equilibrium with thermal radiation.
• In the canonical case of three spatial dimensions, it was previously established that due to quantum buoyancy effects the box floats at some neutral point very close to the horizon.