Relative information entropy in cosmology: The problem of information entanglement

The necessary information to distinguish a local inhomogeneous mass density field from its spatial average on a compact domain of the universe can be measured by relative information entropy. The Kullback-Leibler (KL) formula arises very naturally in this context, however, it provides a very complic...

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Bibliographic Details
Published in:arXiv.org 2016-04
Main Authors: Czinner, Viktor G, Mena, Filipe C
Format: Article
Language:English
Subjects:
Cosmology
Entanglement
Entropy
Entropy (Information theory)
Gravitational fields
Universe
Online Access:Get full text
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Summary:The necessary information to distinguish a local inhomogeneous mass density field from its spatial average on a compact domain of the universe can be measured by relative information entropy. The Kullback-Leibler (KL) formula arises very naturally in this context, however, it provides a very complicated way to compute the mutual information between spatially separated but causally connected regions of the universe in a realistic, inhomogeneous model. To circumvent this issue, by considering a parametric extension of the KL measure, we develop a simple model to describe the mutual information which is entangled via the gravitational field equations. We show that the Tsallis relative entropy can be a good approximation in the case of small inhomogeneities, and for measuring the independent relative information inside the domain, we propose the Rényi relative entropy formula.
ISSN:2331-8422
DOI:10.48550/arxiv.1604.06947