Non-Archimedean character of quantum buoyancy and the generalized second law of thermodynamics

TL;DR

The paper reexamines quantum buoyancy as a mechanism for preserving the generalized second law when lowering entropy-bearing bodies into a black hole. It shows that a fluid-dynamics (Unruh-radiance) description of buoyancy fails away from the horizon and must be replaced by a wave-diffraction treatment, revealing a non-Archimedean buoyancy in the far region and a fluid-like, Archimedean buoyancy near the horizon. Energetic analyses across far, near, and intermediate regions demonstrate that buoyancy alone cannot guarantee the GSL in the intermediate and far regions, though the universal entropy bound S ≤ 2πER/ħ remains a sufficient condition for GSL validity. The authors also find that buoyancy for a single elementary charged particle is negligible and discuss the puzzling absence of N (the number of species) in the bound and holographic principles, arguing for the bound's primacy in safeguarding the GSL, even with numerous particle species.

Abstract

Quantum buoyancy has been proposed as the mechanism protecting the generalized second law when an entropy--bearing object is slowly lowered towards a black hole and then dropped in. We point out that the original derivation of the buoyant force from a fluid picture of the acceleration radiation is invalid unless the object is almost at the horizon, because otherwise typical wavelengths in the radiation are larger than the object. The buoyant force is here calculated from the diffractive scattering of waves off the object, and found to be weaker than in the original theory. As a consequence, the argument justifying the generalized second law from buoyancy cannot be completed unless the optimal drop point is next to the horizon. The universal bound on entropy is always a sufficient condition for operation of the generalized second law, and can be derived from that law when the optimal drop point is close to the horizon. We also compute the quantum buoyancy of an elementary charged particle; it turns out to be negligible for energetic considerations. Finally, we speculate on the significance of the absence from the bound of any mention of the number of particle species in nature.