Multi-Additivity in Kaniadakis Entropy

It is known that Kaniadakis entropy, a generalization of the Shannon-Boltzmann-Gibbs entropic form, is always super-additive for any bipartite statistically independent distributions. In this paper, we show that when imposing a suitable constraint, there exist classes of maximal entropy distribution...

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Bibliographic Details
Published inEntropy (Basel, Switzerland) Vol. 26; no. 1; p. 77
Main Authors Scarfone, Antonio M, Wada, Tatsuaki
Format Journal Article
LanguageEnglish
Published Switzerland MDPI AG 01.01.2024
Subjects
Boundary conditions
Entropy
power-law distributions
Probability distribution
pseudo-additivity
Real numbers
Statistics
κ-entropy
pseudo-additivity
κ-entropy
power-law distributions
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Summary:It is known that Kaniadakis entropy, a generalization of the Shannon-Boltzmann-Gibbs entropic form, is always super-additive for any bipartite statistically independent distributions. In this paper, we show that when imposing a suitable constraint, there exist classes of maximal entropy distributions labeled by a positive real number ℵ>0 that makes Kaniadakis entropy multi-additive, i.e., Sκ[pA∪B]=(1+ℵ)Sκ[pA]+Sκ[pB], under the composition of two statistically independent and identically distributed distributions pA∪B(x,y)=pA(x)pB(y), with reduced distributions pA(x) and pB(y) belonging to the same class.
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ISSN:1099-4300
1099-4300
DOI:10.3390/e26010077