Entropic nonextensivity: a possible measure of complexity

An updated review (corresponding to the inaugural talk delivered at the The International Workshop on Classical and Quantum Complexity and Nonextensive Thermodynamics, Denton, TX, April 3–6, 2000) of nonextensive statistical mechanics and thermodynamics is colloquially presented. Quite naturally the possibility emerges for using the value of q−1 (entropic nonextensivity) as a simple and efficient manner to provide, at least for some classes of systems, some characterization of the degree of what is currently referred to as complexity (M. Gell-Mann, The Quark and the Jaguar, Freeman, New York, 1994). A few historical digressions are included as well.