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.

Relativistic Roots of κ-Entropy

“…In the last two decades, various authors have devoted themselves to the study of both the theoretical foundations of the theory and its applications not only in plasma physics but also in various other areas of the science of complex physical, natural, or artificial statistical systems. Some of these works deal with the H-theorem and the molecular chaos hypothesis [14,15], thermodynamic stability [16,17], Lesche stability [18][19][20][21], the Legendre structure of the resulting thermodynamics [22,23], the thermodynamics of nonequilibrium systems [24], quantum versions of the theory [25][26][27][28], the geometric structure of the theory [29,30], various mathematical aspects of the theory [31][32][33][34][35][36][37][38][39][40][41][42][43][44], etc. On the other hand, specific applications to physical systems have been considered, e.g., cosmic rays [5], relativistic [45] and classical [46] plasmas in presence of external electromagnetic fields, relaxation in relativistic plasmas under wave-particle interactions [47,48], electronic cooling [49], dark energy models , quantum gravity [71][72][73][74]…”