Relative information entropy in cosmology: The problem of information entanglement

Czinner, Viktor and Mena, F. C. (2016) Relative information entropy in cosmology: The problem of information entanglement. PHYSICS LETTERS B, 758. pp. 9-13. ISSN 0370-2693

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Abstract

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 R´enyi relative entropy formula.

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