Multi-Additivity in Kaniadakis Entropy

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  • Antonio M. Scarfone
    Istituto dei Sistemi Complessi—Consiglio Nazionale delle Ricerche (ISC-CNR), c/o Dipartimento di Scienza Applicata e Tecnologia del Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
  • Tatsuaki Wada
    Region of Electrical and Electronic Systems Engineering, Ibaraki University, 4-12-1 Nakanarusawa-cho, Hitachi 316-8511, Ibaraki, Japan

説明

<jats:p>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.</jats:p>

収録刊行物

  • Entropy

    Entropy 26 (1), 77-, 2024-01-17

    MDPI AG

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