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Metaphors, generalizations and unifications are natural and
desirable ingredients of the evolution of scientific theories and
concepts. Physics, in particular, obviously walks along these paths
since its very beginning. This book focuses on nonextensive
statistical mechanics, a current generalization of Boltzmann-Gibbs
(BG) statistical mechanics, one of the greatest monuments of
contemporary physics. Conceived more than 130 years ago by Maxwell,
Boltzmann and Gibbs, the BG theory exhibits uncountable - some of
them impressive - successes in physics, chemistry, mathematics, and
computational sciences, to name a few. Presently, more than two
thousand publications, by over 1800 scientists around the world,
have been dedicated to the nonextensive generalization. Remarkable
applications have emerged, and its mathematical grounding is by now
relatively well established. A pedagogical introduction to its
concepts - nonlinear dynamics, extensivity of the nonadditive
entropy, global correlations, generalization of the standard CLT's,
among others - is presented in this book as well as a selection of
paradigmatic applications in various sciences together with
diversified experimental verifications of some of its
predictions.
- This is the first pedagogical book on the subject, written by
the proponent of the theory
- Presents many applications to interdisciplinary complex
phenomena in virtually all sciences, ranging from physics to
medicine, from economics to biology, through signal and image
processing and others
- Offers a detailed derivation of results, illustrations and for
the first time detailed presentation of Nonextensive Statistical
Mechanics
This book focuses on nonextensive statistical mechanics, a current
generalization of Boltzmann-Gibbs (BG) statistical mechanics.
Conceived nearly 150 years ago by Maxwell, Boltzmann and Gibbs, the
BG theory, one of the greatest monuments of contemporary physics,
exhibits many impressive successes in physics, chemistry,
mathematics, and computational sciences. Presently, several
thousands of publications by scientists around the world have been
dedicated to its nonextensive generalization. A variety of
applications have emerged in complex systems and its mathematical
grounding is by now well advanced. Since the first edition release
thirteen years ago, there has been a vast amount of new results in
the field, all of which have been incorporated in this
comprehensive second edition. Heavily revised and updated with new
sections and figures, the second edition remains the go-to text on
the subject. A pedagogical introduction to the BG theory concepts
and their generalizations - nonlinear dynamics, extensivity of the
nonadditive entropy, global correlations, generalization of the
standard CLT's, complex networks, among others - is presented in
this book, as well as a selection of paradigmatic applications in
various sciences together with diversified experimental
verifications of some of its predictions. Introduction to
Nonextensive Statistical Mechanics is suitable for students and
researchers with an interest in complex systems and statistical
physics.
A great variety of complex phenomena in many scientific fields
exhibit power-law behaviour, reflecting a hierarchical or fractal
structure. Many of these phenomena seem to be susceptible to
description using approaches drawn from thermodynamics or
statistical mechanics, particularly approaches involving the
maximization of entropy. During recent years a good deal of study
has been devoted to a nonextensive generalizations of entropy and
of Boltzmann-Gibbs statistical mechanics and standard laws in a
natural way. The book addresses the interdisciplinary applications
of these ideas, and also on various phenomena that could possibly
be quantitatively describable in terms of these ideas.
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