# 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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The Case for Shifting the Rényi Entropy

- Computer ScienceEntropy
- 2019

A variant of the Rényi entropy definition is introduced that aligns it with the well-known Hölder mean: in the new formulation, the r-th order RéNYi Entropy is the logarithm of the inverse of the R2 mean.

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