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Group entropies: from phase space geometry to entropy functionals via Group Theory

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Jensen, Henrik Jeldtoft and Tempesta, Piergiulio (2018) Group entropies: from phase space geometry to entropy functionals via Group Theory. Entropy, 20 (10). ISSN 1099-4300

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Official URL: http://dx.doi.org/10.3390/e20100804


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Abstract

The entropy of Boltzmann-Gibbs, as proved by Shannon and Khinchin, is based on four axioms, where the fourth one concerns additivity. The group theoretic entropies make use of formal group theory to replace this axiom with a more general composability axiom. As has been pointed out before, generalised entropies crucially depend on the number of allowed degrees of freedom N. The functional form of group entropies is restricted (though not uniquely determined) by assuming extensivity on the equal probability ensemble, which leads to classes of functionals corresponding to sub-exponential, exponential or super-exponential dependence of the phase space volume W on N. We review the ensuing entropies, discuss the composability axiom and explain why group entropies may be particularly relevant from an information-theoretical perspective.


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©2018 by the authors.
This research of P.T. has been partly supported by the research project FIS2015-63966, MINECO, Spain, and by the ICMAT Severo Ochoa project SEV-2015-0554 (MINECO).

Uncontrolled Keywords:Statistical-mechanics; Zeta-functions; Formal group; Generalised entropies; Formal groups; Phase space growth rate
Subjects:Sciences > Physics > Physics-Mathematical models
Sciences > Physics > Mathematical physics
ID Code:50580
Deposited On:21 Dec 2018 19:40
Last Modified:08 Jan 2019 09:34

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