Groups, Information Theory and Einstein's Likelihood Principle

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.

5 pages

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Cited by in corpus (8)

• Uniqueness and characterization theorems for generalized entropies
• Group entropies: from phase space geometry to entropy functionals via group theory
• Approach of complexity in nature: Entropic nonuniqueness
• Multivariate Group Entropies, Super-exponentially Growing Complex Systems and Functional Equations
• On the connection between linear combination of entropies and linear combination of extremizing distributions
• Fisher metric from relative entropy group
• Group theory, entropy and the third law of thermodynamics
• Algebraic structures and deformed Schrödinger equations from groups entropies