Entropy bounds in terms of the w parameter

TL;DR

This paper refines an entropy bound for matter in equilibrium by incorporating the averaged w parameter, approaching the black hole entropy limit without requiring a black hole region.

Contribution

It introduces a strengthened entropy bound involving the averaged w parameter, aligning the bound with black hole thermodynamics when the parameter reaches its causality limit.

Findings

The entropy bound is improved using the averaged w parameter.

When the averaged w equals 1, the entropy bound matches black hole entropy.

The bound can approach the Bekenstein limit even without black holes.

Abstract

In a pair of recent articles [PRL 105 (2010) 041302 - arXiv:1005.1132; JHEP 1103 (2011) 056 - arXiv:1012.2867] two of the current authors have developed an entropy bound for equilibrium uncollapsed matter using only classical general relativity, basic thermodynamics, and the Unruh effect. An odd feature of that bound, S <= A/2, was that the proportionality constant, 1/2, was weaker than that expected from black hole thermodynamics, 1/4. In the current article we strengthen the previous results by obtaining a bound involving the (suitably averaged) w parameter. Simple causality arguments restrict this averaged <w> parameter to be <= 1. When equality holds, the entropy bound saturates at the value expected based on black hole thermodynamics. We also add some clarifying comments regarding the (net) positivity of the chemical potential. Overall, we find that even in the absence of any black hole region, we can nevertheless get arbitrarily close to the Bekenstein entropy.