Hyperentropic systems and the generalized second law of thermodynamics

Abstract

The holographic bound asserts that the entropy $S$ of a system is bounded from above by a quarter of the area ${\cal A}$ of a circumscribing surface measured in Planck areas: $S\leq {\cal A}/4{\ell^2_P}$. This bound is widely regarded a desideratum of any fundamental theory. Moreover, it was argued that the holographic bound is necessary for the validity of the generalized second law (GSL) of thermodynamics. However, in this work we explicitly show that hyperentropic systems (those violating the holographic entropy bound) do exist in higher-dimensional spacetimes. We resolve this apparent violation of the GSL and derive an upper bound on the area of hyperentropic objects.