How far can the generalized second law be generalized?

TL;DR

This paper reviews the development of the generalized second law of thermodynamics, especially its extension to cosmological horizons, and confirms its validity across various models including de Sitter universes with black holes.

Contribution

It demonstrates that the generalized second law holds for a wide range of cosmological models, including those with cosmological horizons lacking well-defined thermal properties.

Findings

GSL is satisfied in models with cosmological horizons.

Numerical solutions confirm the GSL over time.

Black hole and cosmological horizon entropies are comparable.

Abstract

Jacob Bekenstein's identification of black hole event horizon area with entropy proved to be a landmark in theoretical physics. In this paper we trace the subsequent development of the resulting generalized second law of thermodynamics (GSL), especially its extension to incorporate cosmological event horizons. In spite of the fact that cosmological horizons do not generally have well-defined thermal properties, we find that the GSL is satisfied for a wide range of models. We explore in particular the case of an asymptotically de Sitter universe filled with a gas of small black holes as a means of casting light on the relative entropic 'worth' of black hole versus cosmological horizon area. We present some numerical solutions of the generalized total entropy as a function of time for certain cosmological models, in all cases confirming the validity of the GSL.