Hyperentropic systems and the generalized second law of thermodynamics

TL;DR

This paper demonstrates the existence of hyperentropic systems in higher-dimensional spacetimes that violate the holographic bound and shows how the generalized second law of thermodynamics remains valid by deriving an upper bound on their area.

Contribution

It explicitly constructs hyperentropic systems in higher dimensions and resolves their apparent conflict with the GSL by establishing an upper area bound.

Findings

Hyperentropic systems exist in higher-dimensional spacetimes.

The GSL remains valid despite violations of the holographic bound.

An upper bound on the area of hyperentropic objects is derived.

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.