The additivity of the pseudo-additive conditional entropy for a proper Tsallis' entropic index

Abstract

For Tsallis' entropic analysis to the time evolutions of standard logistic map at the Feigenbaum critical point, it is known that there exists a unique value $q^{\ast }$ of the entropic index such that the asymptotic rate $K_q\equiv {\lim }_{t\to \infty }\{S_q(t)-S_q(0)\}/t$ of increase in $S_q(t)$ remains finite whereas $K_q$ vanishes (diverges) for $q>q^{\ast }(q<q^{\ast })$. We show that in spite of the associated whole time evolution cannot be factorized into a product of independent sub-interval time evolutions, the pseudo-additive conditional entropy $S_q(t|0)\equiv \{S_q(t)-S_q(0)\}/\{1+(1-q)S_q(0)\}$ becomes additive when $q=q^{\ast }$. The connection between $K_{q^{\ast }}$ and the rate $K_{q^{\ast }}^{\prime }\equiv S_{q^{\ast }}(t|0)/t$ of increase in the conditional entropy is discussed.

LaTeX2e, elsart, 4 pages, no figure, contributed paper to the Proceedings of the International School and Workshop on Nonextensive Thermodynamics and physical applications, NEXT 2001, 23-30 May 2001, Cagliari (Italy) (Physica A)

References in corpus (1)

• When non-extensive entropy becomes extensive