Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2012-02-15
Physics
Condensed Matter
Statistical Mechanics
9 pages including 1 figure. Invited paper for the Proceedings of the International Symposium on Subnuclear Physics: Past, Pres
Scientific paper
We briefly review a perspective along which the Boltzmann-Gibbs statistical mechanics, the strongly chaotic dynamical systems, and the Schroedinger, Klein-Gordon and Dirac partial differential equations are seen as linear physics, 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 directly related to what is nowadays referred to as complexity, or complex systems. We first discuss a few central points like the distinction between additivity and extensivity, and the Central Limit Theorem as well as the large-deviation theory. Then we comment the case of gravitation (which within the present context corresponds to q {\neq} 1, and to similar nonlinear approaches), with special focus onto the entropy of black holes. Finally we briefly focus on recent nonlinear generalizations of the Schroedinger, Klein-Gordon and Dirac equations, and mention various illustrative predictions, verifications and applications within physics (in both low- and high-energy regimes) as well as out of it.
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