Groups, Information Theory and Einstein's Likelihood Principle

Gabriele Sicuro; Piergiulio Tempesta

doi:10.1103/physreve.93.040101

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arXiv · 1512.00089

Groups, Information Theory and Einstein's Likelihood Principle

Gabriele Sicuro·Piergiulio Tempesta

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Abstract

We propose a unifying picture where the notion of generalized entropy is related to information theory by means of a group-theoretical approach. The group structure comes from the requirement that an entropy be well defined with respect to the composition of independent systems, in the context of a recently proposed generalization of the Shannon-Khinchin axioms. We associate to each member of a large class of entropies a generalized information measure, satisfying the additivity property on a set of independent systems as a consequence of the underlying group law. At the same time, we also show that Einstein's likelihood function naturally emerges as a byproduct of our informational interpretation of (generally nonadditive) entropies. These results confirm the adequacy of composable entropies both in physical and social science contexts.

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Gabriele Sicuro, Piergiulio Tempesta. 2016-04-06. Groups, Information Theory and Einstein's Likelihood Principle. https://doi.org/10.1103/physreve.93.040101

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