1202.3178 (Contantino Tsallis)

From nolinear statistical mechanics to nonlinear quantum mechanics -
Concepts and applications    [PDF]

Contantino Tsallis

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.

View original: http://arxiv.org/abs/1202.3178