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 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.

Sefficiency (sustainable efficiency) of water–energy–food entangled systems

Supplemental data for this article can be accessed at http://dx.doi.org/10.1080/07900627.2015.1070091. It includes an easy-to-use spreadsheet that calculates the efficiencies used in this paper, that is Sefficiency with energy considerations.

Rede ecológica para a deteção e estudo de aves marinhas arrojadas REDEMAR-AVES (costa norte portuguesa)

Dissertação de mestrado em Ecologia