A proof of the Bekenstein bound for any strength of gravity through holography

TL;DR

This paper proves the Bekenstein entropy bound for any gravitational strength using holography, linking system size, energy, and entropy through a lower size limit derived from holographic principles.

Contribution

It provides a general proof of the Bekenstein bound applicable at all gravity strengths, based on a holographic lower size limit and its implications.

Findings

Established a lower size limit l* from holography for defining system quantities.

Connected the size limit to the proliferation of species problem.

Explored implications for viscosity to entropy density ratio in various fluids.

Abstract

The universal entropy bound of Bekenstein is considered, at any strength of the gravitational interaction. A proof of it is given, provided the considered general-relativistic spacetimes allow for a meaningful and inequivocal definition of the quantities which partecipate to the bound (such as system's energy and radius). This is done assuming as starting point that, for assigned statistical-mechanical local conditions, a lower-limiting scale l* to system's size definitely exists, being it required by holography through its semiclassical formulation as given by the generalized covariant entropy bound. An attempt is made also to draw some possible general consequences of the l* assumption with regards to the proliferation of species problem and to the viscosity to entropy density ratio. Concerning the latter, various fluids are considered including systems potentially relevant, to some extent, to the quark-gluon plasma case.