Configuration entropy in the soft wall AdS/QCD model and the Wien law

TL;DR

This paper uses configuration entropy within the soft wall AdS/QCD model to analyze the stability of black hole geometries at different temperatures, revealing a Wien law-like behavior in the energy density distribution.

Contribution

It introduces a regularized energy density for AdS black holes and links the configuration entropy to black hole stability and a Wien law analogy in the deconfined phase.

Findings

Configuration entropy correlates with black hole stability.

Regularized energy density exhibits Wien law-like behavior.

Maximum energy density momentum scales linearly with temperature.

Abstract

The soft wall AdS/QCD holographic model provides simple estimates for the spectra of light mesons and glueballs satisfying linear Regge trajectories. It is also an interesting tool to represent the confinement/deconfinement transition of a gauge theory, that is pictured as a Hawking-Page transition from a dual geometry with no horizon to a black hole space. A very interesting tool to analyze stability of general physical systems that are localized in space is the configuration (or complexity) entropy (CE). This quantity, inspired in Shannon information entropy, is defined in terms of the energy density of the system in momentum space. The purpose of this work is to use the CE to investigate the stability of the soft wall background as a function of the temperature. A nontrivial aspect is that the geometry is an anti-de Sitter black hole, that has a singular energy density. In order to make it possible to calculate the CE, we first propose a regularized form for the black hole energy density. Then, calculating the CE, it is observed that its behavior is consistently related to the black hole instability in anti-de Sitter space. Another interesting result that emerges from this analysis is that the regularized energy density shows a behavior similar to the Wien law, satisfied by black body radiation. That means: the momentum $ k_{max} $ where the energy density is maximum, varies with the temperature $T$ obeying the relation: $ T / k_{max} = constant $ in the deconfined phase.