Extensive Entropy Functionals and Non-ergodic Random Walks.

According to Tsallis’ seminal book on complex systems: “an entropy of a system is extensive if, for a large number n of its elements, the entropy is (asymptotically) proportional to n ". According to whether the focus is on the system or on the entropy, an entropy is extensive for a given system or a system is extensive for a given entropy. Yet, exhibiting the right classes of random sequences that are extensive for the right entropy is far from being trivial, and is mostly a new area for generalized entropies. This paper aims at giving some examples or classes of random walks that are extensive for Tsallis entropy.