Higher-dimensional violations of the holographic entropy bound

Understand

The holographic bound, $S<=A/4{\ell^2_P}$, asserts that the entropy $S$ of a system is bounded from above by a quarter of the area $A$ of a circumscribing surface measured in Planck areas.

• This bound is widely regarded as part of the elusive fundamental theory of nature.
• In fact, the bound is known to be valid for generic weakly gravitating isolated systems in {\it three} spatial dimensions.
• Nevertheless, the entropy content of a physical system is expected to be an increasing function of the number of spatial dimensions (the more the dimensions, the more ways there are to split up a given amount of energy).