Publication: Groups, information theory, and Einstein's likelihood principle
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2016-04-06
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American Physical Society
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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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©2016 American Physical Society.
We thank Francesco Toppan and Constantino Tsallis for useful discussions. G.S. acknowledges the financial support of the John Templeton Foundation. The research of P.T. has been partly supported by the project FIS2015-63966, MINECO, Spain, and by the ICMAT Severo Ochoa project SEV-2015-0554 (MINECO).
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