Mathematical Foundations Of Nonextensive Statistical Mechanics
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Mathematical Foundations Of Nonextensive Statistical Mechanics
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Author : Sabir Umarov
language : en
Publisher: World Scientific
Release Date : 2022-03-03
Mathematical Foundations Of Nonextensive Statistical Mechanics written by Sabir Umarov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-03 with Science categories.
The book is devoted to the mathematical foundations of nonextensive statistical mechanics. This is the first book containing the systematic presentation of the mathematical theory and concepts related to nonextensive statistical mechanics, a current generalization of Boltzmann-Gibbs statistical mechanics introduced in 1988 by one of the authors and based on a nonadditive entropic functional extending the usual Boltzmann-Gibbs-von Neumann-Shannon entropy. Main mathematical tools like the q-exponential function, q-Gaussian distribution, q-Fourier transform, q-central limit theorems, and other related objects are discussed rigorously with detailed mathematical rational. The book also contains recent results obtained in this direction and challenging open problems. Each chapter is accompanied with additional useful notes including the history of development and related bibliographies for further reading.
Mathematical Foundations Of Nonextensive Statistical Mechanics
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Author : Sabir Umarov
language : en
Publisher:
Release Date : 2022
Mathematical Foundations Of Nonextensive Statistical Mechanics written by Sabir Umarov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with Electronic books categories.
Introduction To Nonextensive Statistical Mechanics
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Author : Constantino Tsallis
language : en
Publisher: Springer Nature
Release Date : 2023-01-30
Introduction To Nonextensive Statistical Mechanics written by Constantino Tsallis and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-30 with Science categories.
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.
Introduction To Nonextensive Statistical Mechanics
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Author : Constantino Tsallis
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-03-11
Introduction To Nonextensive Statistical Mechanics written by Constantino Tsallis and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-03-11 with Science categories.
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
Mathematical Foundations Of Statistical Mechanics
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Author : Aleksandr I?Akovlevich Khinchin
language : en
Publisher: Courier Corporation
Release Date : 1949-01-01
Mathematical Foundations Of Statistical Mechanics written by Aleksandr I?Akovlevich Khinchin and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1949-01-01 with Mathematics categories.
Phase space, ergodic problems, central limit theorem, dispersion and distribution of sum functions. Chapters include Geometry and Kinematics of the Phase Space; Ergodic Problem; Reduction to the Problem of the Theory of Probability; Application of the Central Limit Theorem; Ideal Monatomic Gas; The Foundation of Thermodynamics; and more.
Chaos Nonlinearity Complexity
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Author : Ashok Sengupta
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-09-25
Chaos Nonlinearity Complexity written by Ashok Sengupta and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-09-25 with Computers categories.
This book explores non-extensive statistical mechanics in non-equilibrium thermodynamics, and presents an overview of the strong nonlinearity of chaos and complexity in natural systems, drawing on relevant mathematics from topology, measure-theory, inverse and ill-posed problems, set-valued analysis, and nonlinear functional analysis. It offers a self-contained theory of complexity and complex systems as the steady state of non-equilibrium systems, denoting a homeostatic dynamic equilibrium between stabilizing order and destabilizing disorder.
Advances In Chemical Physics Volume 162
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Author : Stuart A. Rice
language : en
Publisher: John Wiley & Sons
Release Date : 2017-08-17
Advances In Chemical Physics Volume 162 written by Stuart A. Rice and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-17 with Science categories.
The Advances in Chemical Physics series provides the chemical physics field with a forum for critical, authoritative evaluations of advances in every area of the discipline. • This is the only series of volumes available that presents the cutting edge of research in chemical physics. • Includes contributions from experts in this field of research. • Contains a representative cross-section of research that questions established thinking on chemical solutions • Structured with an editorial framework that makes the book an excellent supplement to an advanced graduate class in physical chemistry or chemical physics
Concepts And Recent Advances In Generalized Information Measures And Statistics
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Author : Andres M. Kowalski, Raul D. Rossignoli and Evaldo M. F. Curado
language : en
Publisher: Bentham Science Publishers
Release Date : 2013-12-13
Concepts And Recent Advances In Generalized Information Measures And Statistics written by Andres M. Kowalski, Raul D. Rossignoli and Evaldo M. F. Curado and has been published by Bentham Science Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-13 with Science categories.
Since the introduction of the information measure widely known as Shannon entropy, quantifiers based on information theory and concepts such as entropic forms and statistical complexities have proven to be useful in diverse scientific research fields. This book contains introductory tutorials suitable for the general reader, together with chapters dedicated to the basic concepts of the most frequently employed information measures or quantifiers and their recent applications to different areas, including physics, biology, medicine, economics, communication and social sciences. As these quantifiers are powerful tools for the study of general time and data series independently of their sources, this book will be useful to all those doing research connected with information analysis. The tutorials in this volume are written at a broadly accessible level and readers will have the opportunity to acquire the knowledge necessary to use the information theory tools in their field of interest.
Compound Systems In Nonextensive Statistical Mechanics And Manganites
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Author : Felipe Américo Reyes Navarro
language : en
Publisher: Cambridge Scholars Publishing
Release Date : 2022-07-21
Compound Systems In Nonextensive Statistical Mechanics And Manganites written by Felipe Américo Reyes Navarro and has been published by Cambridge Scholars Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-07-21 with Science categories.
This book presents insights into manganese oxides, which are materials with important technological applications such as magnetic refrigeration and magnetic sensors. It provides many mathematical proofs carried out in a didactic and elegant way; some of them use, for example, the method of mathematical induction. The book will be of interest to both researchers of physical sciences and the general reader interested in the subject.
Nonextensive Statistical Mechanics And Its Applications
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Author : Sumiyoshi Abe
language : en
Publisher: Springer
Release Date : 2008-01-11
Nonextensive Statistical Mechanics And Its Applications written by Sumiyoshi Abe and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-11 with Science categories.
Nonextensive statistical mechanics is now a rapidly growing field and a new stream in the research of the foundations of statistical mechanics. This generalization of the well-known Boltzmann--Gibbs theory enables the study of systems with long-range interactions, long-term memories or multi-fractal structures. This book consists of a set of self-contained lectures and includes additional contributions where some of the latest developments -- ranging from astro- to biophysics -- are covered. Addressing primarily graduate students and lecturers, this book will also be a useful reference for all researchers working in the field.