Abstract:In this paper, we investigate the mixture arc on generalized statistical manifolds. We ensure that the generalization of the mixture arc is well defined and we are able to provide a generalization of the open exponential arc and its properties. We consider the model of a ϕ-family of distributions to describe our general statistical model.
We propose a generalization of the quantum relative entropy by considering the geodesic on a manifold formed by all the invertible density matrices P. This geodesic is defined from a deformed exponential function ϕ which allows to work with a wider class of families of probability distributions. Such choice allows important flexibility in the statistical model. We show and discuss some properties of this proposed generalized quantum relative entropy.2020 Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.