A statistical measure of complexity with nonextensive entropy

A statistical measure of complexity utilising the concept of entropy or information is proposed. Our way in this study is to use a nonextensive entropy instead of an extensive (additive) Shannon entropy in the definition, but can be characterised as a difference between the qth-order Rényi entropy and the second one. Furthermore, we devise a conditional, joint, and mutual complexity measure as a coherent possibility. The behavior of the measure for the logistic map shows that it is more sensitive to nonextensivity at the transition point ac∼3.8284… than any other values when 0<q<1.