A new class of entropic information measures, formal group theory and information geometry

Abstract

In this work, we study generalized entropies and information geometry in a group-theoretical framework. We explore the conditions that ensure the existence of some natural properties and at the same time of a group-theoretical structure for a large class of entropies. In addition, a method for defining new entropies, using previously known ones with some desired group-theoretical properties is proposed. In the second part of this work, the information geometrical counterpart of the previous construction is examined and a general class of divergences are proposed and studied. Finally, a method of constructing new divergences from known ones is discussed; in particular, some results concerning the Riemannian structure associated with the class of divergences under investigation are formulated.

arXiv comment17 pages

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• Multivariate Group Entropies, Super-exponentially Growing Complex Systems and Functional Equations
• Permutation group entropy: a new route to complexity for real-valued processes
• On the probability of the Condorcet Jury Theorem or the Miracle of Aggregation
• Complexity-based permutation entropies: from deterministic time series to white noise