Multi-Additivity in Kaniadakis Entropy.

Abstract

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.