Groups, Information Theory and Einstein's Likelihood Principle

TL;DR

This paper introduces a group-theoretical framework linking generalized entropy to information theory, showing that Einstein's likelihood naturally arises from this approach and confirming the relevance of composable entropies across disciplines.

Contribution

It unifies generalized entropy and information theory through a group-theoretical approach, connecting Einstein's likelihood to nonadditive entropies.

Findings

Generalized entropies are associated with a generalized information measure.

Einstein's likelihood function emerges from the informational interpretation.

The framework confirms the applicability of composable entropies in various fields.

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.