title: 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.
authors.affiliation: Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud, 150, 22290-180, Rio de Janeiro, Brazil.
authors.forename: Gabriele
authors.initials: G
authors.lastname: Sicuro
authors.affiliation: Departamento de Física Teórica II (Métodos Matemáticos de la física), Facultad de Físicas, Universidad Complutense de Madrid, 28040 Madrid, Spain and Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM), Calle Nicolás Cabrera, No. 13-15, 28049 Madrid, Spain.
authors.forename: Piergiulio
authors.initials: P
authors.lastname: Tempesta