### Marolf on Entropy Bounds

Don Marolf was in town this week, and talked about his work with Sorkin on Entropy Bounds. The Bekenstein bound,

on the entropy of an object of energy $E$ and size $R$, ($\alpha$ is some dimensionless number) and the Holographic bound

on the entropy in a region of area $A$ (a more precise formulation of this latter bound is due to Bousso) have been much bruited about since they were proposed.

The validity of these bounds ultimately rests on an argument involving the consistency of the generalized Second Law. Were it possible to have an object which violated one of these bounds, one could either drop it into a blackhole, or accrete matter onto it to form a blackhole and the resulting process would produce a net decrease of the total entropy in the universe.

What Marolf and Sorkin note is that such highly entropic object are necessarily an important component of the Hawking radiation. In a thermal ensemble at temperature $T_{\mathrm{BH}}= (4\pi R_{\mathrm{BH}})^{-1}$, the probablility of finding such an object is proportional to $e^{-\beta F}$, where $F$ is the free energy, $F=E-TS$. Even when the temperature of the blackhole is low, whenever $S$ is large enough to potentially violate one of these bounds, these objects become an important component of the thermal ensemble.

According to their analysis, any process in which — if one neglected the Hawking radiation — the Generalized Second Law would be violated, will either be forbidden or will be accompanied by the emission of enough of these guys in the Hawking radiation that the total entropy increases, and the Second Law is satisfied.

Admittedly, I’ve never been a big fan of Holography as a putative fundamental principle of quantum gravity, but Marolf and Sorkin’s argument seems to have unhitched it from its grounding in the Generalized Second Law. That connection was, heretofore, the main reason for believing in Holography.

Posted by distler at December 3, 2003 11:33 PM
## Re: Marolf on Entropy Bounds

There is an interesting proposal by Andreas Karch. With certain assumtions, he showed that the entropy bound implies the viscosity bound. Moreover, this relation seems true even beyond the assumptions that he made. An interesting point is that the tabletop experiments could test this. The viscosity of superfluid He

_{4}misses the bound only by a factor of 10.