Composition law of κ-entropy for statistically independent systems

The intriguing and still open question concerning the composition law of κ--entropy is here reconsidered and solved. It is shown that, for a statistical system described by a probability distribution, made up of two statistically independent subsystems, described through the probability distributions p and q respectively, the joint κ--entropy S(q,p) can be obtained starting from the κ--entropies, S(q) and S(P), and additionally from the κ--entropic functionals S(q/e), S(p/e) , being e the κ-Napier number. The composition law of the κ-entropy is given in closed form and emerges as a one-parameter generalization of the ordinary additivity law of Boltzmann-Shannon entropy recovered in the κ→0 limit.