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 distributions labeled by a positive real number ℵ > 0 that makes Kaniadakis entropy multi-additive, i.e., S κ [ p A ∪ B ] = (1 + ℵ) S κ [ p A ] + S κ [ p B ] , under the composition of two statistically independent and identically distributed distributions p A ∪ B (x , y) = p A (x) p B (y) , with reduced distributions p A (x) and p B (y) belonging to the same class. [ABSTRACT FROM AUTHOR]