• Corpus ID: 11487327

Entropy operates in non-linear semifields

@article{ValverdeAlbacete2017EntropyOI,
  title={Entropy operates in non-linear semifields},
  author={Francisco J. Valverde-Albacete and Carmen Pel{\'a}ez-Moreno},
  journal={ArXiv},
  year={2017},
  volume={abs/1710.04728}
}
We set out to demonstrate that the R\'enyi entropies with parameter $\alpha$ are better thought of as operating in a type of non-linear semiring called a positive semifield. We show how the R\'enyi's postulates lead to Pap's g-calculus where the functions carrying out the domain transformation are Renyi's information function and its inverse. In its turn, Pap's g-calculus under R\'enyi's information function transforms the set of positive reals into a family of semirings where "standard… 

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