When Shannon and Khinchin meet Shore and Johnson: equivalence of information theory and statistical inference axiomatics

Abstract

We propose a unified framework for both Shannon-Khinchin and Shore-Johnson axiomatic systems. We do it by rephrasing Shannon-Khinchine axioms in terms of generalized arithmetics of Kolmogorov and Nagumo. We prove that the two axiomatic schemes yield identical classes of entropic functionals -- Uffink class of entropies. This allows to re-establish the entropic parallelism between information theory and statistical inference that has seemed to be "broken" by the use of non-Shannonian entropies.

6 pages, this version was accepted to Phys. Rev. E

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• On the Relativity of Quantumness as Implied by Relativity of Arithmetic and Probability
• Dimensional measures of generalized entropy
• Learn your entropy from informative data: an axiom ensuring the consistent identification of generalized entropies
• On nonlinear compression costs: when Shannon meets Rényi