Groups, information theory, and Einstein's likelihood principle
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...
| Autores: | , |
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| Tipo de documento: | artigo |
| Data de publicação: | 2016 |
| País: | España |
| Recursos: | Universidad Complutense de Madrid (UCM) |
| Repositório: | Docta Complutense |
| Idioma: | inglês |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/24471 |
| Acesso em linha: | https://hdl.handle.net/20.500.14352/24471 |
| Access Level: | Acceso aberto |
| Palavra-chave: | 51-73 Generalized entropies Superstatistics Statistics Renyi Física-Modelos matemáticos |
| Resumo: | 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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