• DOI:10.1007/JHEP12(2010)033
• Corpus ID: 53313858

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

@article{Hod2011QuantumBG,
  title={Quantum buoyancy, generalized second law, and higher-dimensional entropy bounds},
  author={Shahar Hod},
  journal={Journal of High Energy Physics},
  year={2011},
  volume={2010},
  pages={1-12}
}

• S. Hod
• Published 17 January 2011
• Physics
• Journal of High Energy Physics

Bekenstein haspresented evidencefor theexistenceofa universalupperbound of magnitude 2πR/ℏc to the entropy-to-energy ratio S/E of an arbitrary 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. We find here that the significance of quantum buoyancy increases dramatically with the number D of spatial dimensions. In particular, we find that the neutral (floating) point of the box lies near the horizon only if its length b is large enough such that b/bC > F(D), where bC is the Compton length of the body and F(D) ∼ DD/2 ≫ 1 for D ≫ 1. A consequence is that quantum buoyancy severely restricts our ability to deduce the universal entropy bound from the generalized second law of thermodynamics in higher-dimensional spacetimes with D ≫ 1. Nevertheless, we find that the universal entropy bound is always a sufficient condition for operation of the generalized second law in this type of gedanken experiments.