2012/02/14 by C. Tsallis, Contantino Tsallis, Tsallis, Contantino
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Cosmology and Gravitation Theories #Data Analysis #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #Quantum Mechanics and Applications #Statistical Mechanics (cond-mat.stat-mech) #Statistical Mechanics and Entropy #Statistics and Probability (physics.data-an) #cond-mat.stat-mech #hep-ph #physics.data-an
paper · pdf · doi:10.48550/arxiv.1202.3178
9 pages including 1 figure. Invited paper for the Proceedings of the International Symposium on Subnuclear Physics: Past, Present and Future, held at the Pontifical Academy of Sciences (Vatican, 30 October to 2 November 2011)
openalex publication_date 2012/02/14 · arxiv created 2012/02/15 · arxiv updated 2012/02/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 ≠ 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 ≠ 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.