When Shannon and Khinchin meet Shore and Johnson: Equivalence of information theory and statistical inference axiomatics.
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- Also identified by DOI 10.1103/PhysRevE.101.042126.
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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-the 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.