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Tempesta, Piergiulio (2016) Formal groups and Zentropies. Proceedings of the Royal Society of London Series A  Mathematical Physical and Engineering Sciences, 472 (2195). ISSN 13645021

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Official URL: http://dx.doi.org/10.1098/rspa.2016.0143
URL  URL Type 

http://rspa.royalsocietypublishing.org  Publisher 
https://arxiv.org/abs/1507.07436  Organisation 
Abstract
We shall prove that the celebrated Renyi entropy is the first example of a new family of infinitely many multiparametric entropies. We shall call them the Zentropies. Each of them, under suitable hypotheses, generalizes the celebrated entropies of Boltzmann and Renyi. A rucial aspect is that every Zentropy is composable (Tempesta 2016 Ann. Phys. 365, 180197. (doi: 10.1016/j.aop.2015.08.013)). This property means that the entropy of a system which is composed of two or more independent systems depends, in all the associated probability space, on the choice of the two systems only. Further properties are also required to describe the composition process in terms of a group law. The composability axiom, introduced as a generalization of the fourth ShannonKhinchin axiom (postulating additivity), is a highly non trivial requirement. Indeed, in the traceform class, the Boltzmann entropy and Tsallis entropy are the only known composable cases. However, in the nontrace form class, the Zentropies arise as new entropic functions possessing the mathematical properties necessary for informationtheoretical applications, in both classical and quantum contexts. From a mathematical point of view, composability is intimately related to formal group theory of algebraic topology. The underlying grouptheoretical structure determines crucially the statistical properties of the corresponding entropies.
Item Type:  Article 

Additional Information:  This work has been partly supported by the research project FIS201563966, MINECO, Spain, and by the ICMAT Severo Ochoa project SEV20150554 (MINECO). 
Uncontrolled Keywords:  Group laws; Polynomials; Bernoulli 
Subjects:  Sciences > Physics > PhysicsMathematical models Sciences > Physics > Mathematical physics 
ID Code:  41495 
Deposited On:  23 Feb 2017 12:56 
Last Modified:  10 Dec 2018 15:09 
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