![]() ![]() Recognized as such - together with mechanics (classical, quantum, relativistic), electromagnetism and thermodynamics -, it is one of the mandatory theories studied at virtually all the intermediate-and advanced-level courses of physics around the world. Statistical mechanics constitutes one of the pillars of contemporary physics. Nonadditive entropy and nonextensive statistical mechanics -an overview after 20 yearsĬentro Brasileiro de Pesquisas Físicas and National Institute of Science and Technology for Complex Systems Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro, Brazil and Santa Fe Institute 1399 Hyde Park Road, Santa Fe, NM 87501, USA Nonadditive entropy Nonextensive statistical mechanics Complex systems Nonlinear dynamics Various theoretical, experimental, observational and computational aspects will be addressed. In the present occasion, after 20 years of the 1988 proposal, we undertake here an overview of some selected successes of the approach, and of some interesting points that still remain as open questions. It even poses deep challenges at the level of the CLT. This peculiarity has sensible effects at all physical micro-, meso-and macroscopic levels. This fact creates a quite novel situation with regard to typical BG systems, which generically have a positive value for this central nonlinear dynamical quantity. Indeed, in such systems, the maximal Lyapunov exponent vanishes in the thermodynamic limit N → ∞. Such appears to be, for instance, the case in classical long-range-interacting many-body Hamiltonian systems (at the so-called quasi-stationary state). The extension of the standard concepts is intended to be useful in those "pathological", and nevertheless very frequent, cases where the basic assumptions (molecular chaos hypothesis, ergodicity) for applicability of the BG theory would be violated. Within this complex ongoing frame, a possible generalization of the BG theory was advanced in 1988 (C.T., J. In many circumstances, the ubiquitous efects of the CLT, with its Gaussian attractors (in the space of the distributions of probabilities), are present. In the case of statistical mechanics, the standard theory - hereafter referred to as the Boltzmann-Gibbs (BG) statistical mechanics - exhibits highly relevant connections at a variety of microscopic, mesoscopic and macroscopic physical levels, as well as with the theory of probabilities (in particular, with the Central Limit Theorem, CLT ). As it normally happens with such basic scientific paradigms, it is placed at a crossroads of various other branches of knowledge. 47 (1961) 724.Statistical mechanics constitutes one of the pillars of contemporary physics. 29 S.Yatsiv: Advances in Quantum Electronics, ed.23 A.Messiah: Quantum Mechanics, (English Translation) Vol.M.Lifshitz: Statistical Physics, (English Translation) Pergamon Press, London, 1958. 20 K.Yoshida: Lectures on Differential and Integral Equations, Interscience Publ.Sz.Nagy: Functional Analysis, (English Translation) Fredelich Angars Publ. 18 D.Hilbert: Grundzuge einer Allgemeinen Theorie der Linearen Integralgleichungen, Fortschr.17 M.Born and E.Wolf: Principles of Optics, Pergamon Press, London, 1959.16 D.Middleton: An Introduction to Statistical Communication Theory, McGraw-Hill Book Co., New York, 1960.L.Root: An Introduction to Random Signals and Noise, McGraw-Hill Book Co., New York, 1958. 14 H.Cramér: Mathematical Methods of Statistics, Princeton Univ.13 H.Gamo: Matrix Treatment of Partial Coherence, Progress in Optics, Vol.11 D.Gabor: Light and Information, Astronomical Optics and Related Subjects, ed.3 M.Planck: Vorlesungen uber die Theorie der Warmestrahlung, 2nd Ed., Leipzig, 1913 The Theory of Heat Radiation, (English Translation), Dover Publ., New York, 1959.2, Thomas Nelson and Sons, Ltd., London, 1953 Harper Brothers, New York, 1960. 1 SirEdmundWhittaker: A History of the Theories of Aether and Electricity, Vol. ![]()
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