Relative information entropy in cosmology: The problem of information entanglement

• Autor(a) principal: Czinner, Viktor G.
• Data de Publicação: 2016
• Outros Autores: Mena, Filipe C.
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/1822/41614
• topic: Cosmic inhomogeneities; Information entropy; Large scale structure; Ciências Naturais::Ciências Físicas; Ciências Naturais::Matemáticas; Science & Technology

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.