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We briefly review a perspective along which the Boltzmann-Gibbs statisticalmechanics, the strongly chaotic dynamical systems, and the Schroedinger,Klein-Gordon and Dirac partial differential equations are seen as linearphysics, and are characterized by an index q = 1. We exhibit in what sense q{\neq} 1 yields nonlinear physics, which turn out to be quite rich and directlyrelated to what is nowadays referred to as complexity, or complex systems. Wefirst discuss a few central points like the distinction between additivity andextensivity, and the Central Limit Theorem as well as the large-deviationtheory. Then we comment the case of gravitation (which within the presentcontext corresponds to q {\neq} 1, and to similar nonlinear approaches), withspecial focus onto the entropy of black holes. Finally we briefly focus onrecent nonlinear generalizations of the Schroedinger, Klein-Gordon and Diracequations, and mention various illustrative predictions, verifications andapplications within physics (in both low- and high-energy regimes) as well asout of it.

From nolinear statistical mechanics to nonlinear quantum mechanics - Concepts and applications