Relative information entropy in cosmology: The problem of information entanglement

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 Rényi relative entropy formula.

6 pages, 3 figures, to appear in Phys. Lett. B

References in corpus (4)

• Zeroth Law compatibility of non-additive thermodynamics
• Multiscale cosmology and structure-emerging Dark Energy: A plausibility analysis
• Information Entropy in Cosmology
• Kullback-Leibler entropy and Penrose conjecture in the Lemaitre-Tolman-Bondi model

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