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

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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.

P. Jizba, J. Korbel, When Shannon and Khinchin meet Shore and Johnson: Equivalence of information theory and statistical inference axiomatics, Phys. Rev. E 101 (2020) 042126