Mathematical Foundations Of Nonextensive Statistical Mechanics

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Mathematical Foundations Of Nonextensive Statistical Mechanics

Author : Sabir Umarov
Publisher : World Scientific
ISBN 13 : 9811245177
Total Pages : 336 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Mathematical Foundations Of Nonextensive Statistical Mechanics by : Sabir Umarov

Download or read book Mathematical Foundations Of Nonextensive Statistical Mechanics written by Sabir Umarov and published by World Scientific. This book was released on 2022-03-03 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Sabir Umarov
Publisher :
ISBN 13 : 9789811245152
Total Pages : 340 pages
Book Rating : 4.2/5 (451 download)

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Book Synopsis Mathematical Foundations of Nonextensive Statistical Mechanics by : Sabir Umarov

Download or read book Mathematical Foundations of Nonextensive Statistical Mechanics written by Sabir Umarov and published by . This book was released on 2022 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Introduction to Nonextensive Statistical Mechanics

Author : Constantino Tsallis
Publisher : Springer Science & Business Media
ISBN 13 : 0387853588
Total Pages : 389 pages
Book Rating : 4.3/5 (878 download)

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Book Synopsis Introduction to Nonextensive Statistical Mechanics by : Constantino Tsallis

Download or read book Introduction to Nonextensive Statistical Mechanics written by Constantino Tsallis and published by Springer Science & Business Media. This book was released on 2009-03-11 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Introduction to Nonextensive Statistical Mechanics

Author : Constantino Tsallis
Publisher : Springer Nature
ISBN 13 : 3030795691
Total Pages : 575 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Introduction to Nonextensive Statistical Mechanics by : Constantino Tsallis

Download or read book Introduction to Nonextensive Statistical Mechanics written by Constantino Tsallis and published by Springer Nature. This book was released on 2023-01-30 with total page 575 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

New Trends in Statistical Physics of Complex Systems

Author : Antonio M. Scarfone
Publisher : MDPI
ISBN 13 : 3038974692
Total Pages : 203 pages
Book Rating : 4.0/5 (389 download)

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Book Synopsis New Trends in Statistical Physics of Complex Systems by : Antonio M. Scarfone

Download or read book New Trends in Statistical Physics of Complex Systems written by Antonio M. Scarfone and published by MDPI. This book was released on 2019-01-28 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a printed edition of the Special Issue "New Trends in Statistical Physics of Complex Systems" that was published in Entropy

Nonextensive Entropy

Author : Murray Gell-Mann
Publisher : Oxford University Press, USA
ISBN 13 : 0195159772
Total Pages : 439 pages
Book Rating : 4.1/5 (951 download)

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Book Synopsis Nonextensive Entropy by : Murray Gell-Mann

Download or read book Nonextensive Entropy written by Murray Gell-Mann and published by Oxford University Press, USA. This book was released on 2004 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: Preface, Murray Gell-Mann and Constantino Tsallis. Nonextensive Statistical Mechanics: Construction and Physical Interpretation, Constantino Tsallis. Generalized Nonadditive Information Theory and Quantum Entanglement, Sumiyoshi Abe. Unifying Laws in Multidisciplinary Power-Law Phenomena: Fixed-Point Universality and Nonextensive Entropy, Alberto Robledo. Nonextensive Entropies and Sensitivity to Initial Conditions of Complex Systems, Marcelo L. Lyra. Numerical Analysis of Conservative Maps: A Possible Foundation of Nonextensive Phenomena, Fulvio Baldovin. Nonextensive Effects in Hamiltonian S.

Mathematical Foundations of Statistical Mechanics

Author : Aleksandr I?Akovlevich Khinchin
Publisher : Courier Corporation
ISBN 13 : 0486601471
Total Pages : 210 pages
Book Rating : 4.4/5 (866 download)

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Book Synopsis Mathematical Foundations of Statistical Mechanics by : Aleksandr I?Akovlevich Khinchin

Download or read book Mathematical Foundations of Statistical Mechanics written by Aleksandr I?Akovlevich Khinchin and published by Courier Corporation. This book was released on 1949-01-01 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Anomalous Transport: Applications, Mathematical Perspectives, and Big Data

Author : Ralf Metzler
Publisher : Frontiers Media SA
ISBN 13 : 2889663655
Total Pages : 221 pages
Book Rating : 4.8/5 (896 download)

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Book Synopsis Anomalous Transport: Applications, Mathematical Perspectives, and Big Data by : Ralf Metzler

Download or read book Anomalous Transport: Applications, Mathematical Perspectives, and Big Data written by Ralf Metzler and published by Frontiers Media SA. This book was released on 2021-01-08 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Nonextensive Statistical Mechanics and Its Applications

Author : Sumiyoshi Abe
Publisher : Springer
ISBN 13 : 354040919X
Total Pages : 280 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Nonextensive Statistical Mechanics and Its Applications by : Sumiyoshi Abe

Download or read book Nonextensive Statistical Mechanics and Its Applications written by Sumiyoshi Abe and published by Springer. This book was released on 2008-01-11 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Interdisciplinary Aspects of Turbulence

Author : Wolfgang Hillebrandt
Publisher : Springer Science & Business Media
ISBN 13 : 9783540789604
Total Pages : 353 pages
Book Rating : 4.7/5 (896 download)

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Book Synopsis Interdisciplinary Aspects of Turbulence by : Wolfgang Hillebrandt

Download or read book Interdisciplinary Aspects of Turbulence written by Wolfgang Hillebrandt and published by Springer Science & Business Media. This book was released on 2008-11-20 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by experts from geophysics, astrophysics and engineering, this unique book on the interdisciplinary aspects of turbulence offers recent advances in the field and covers everything from the very nature of turbulence to some practical applications.

The Physics of Complex Systems

Author : Franco Mallamace
Publisher : IOS Press
ISBN 13 : 9781586034450
Total Pages : 648 pages
Book Rating : 4.0/5 (344 download)

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Book Synopsis The Physics of Complex Systems by : Franco Mallamace

Download or read book The Physics of Complex Systems written by Franco Mallamace and published by IOS Press. This book was released on 2004 with total page 648 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is widely known that complex systems and complex materials comprise a major interdisciplinary scientific field that draws on mathematics, physics, chemistry, biology, and medicine as well as such social sciences as economics. The role of statistical physics in this new field has been expanding. Statistical physics has shown how phenomena and processes in different research areas that have long been assumed to be unrelated can have a common description. Through the application of statistical physics, methods developed for studying order phenomena in simple systems and processes have been generalized to more complex systems. This volume focuses on recent advances and perspectives in the physics of complex systems and provides both an overview of the field and a more detailed examination of the new ideas and unsolved problems that are currently attracting the attention of researchers. This book should be a useful reference work for anyone interested in this area, whether beginning graduate student or advanced research professional. It provides up-to-date reviews on cutting-edge topics compiled by leading authorities and is designed to both broaden the reader's competence within their own field and encourage the exploration of new problems in related fields.

Chaos, Nonlinearity, Complexity

Author : Ashok Sengupta
Publisher : Springer Science & Business Media
ISBN 13 : 3540317562
Total Pages : 373 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Chaos, Nonlinearity, Complexity by : Ashok Sengupta

Download or read book Chaos, Nonlinearity, Complexity written by Ashok Sengupta and published by Springer Science & Business Media. This book was released on 2006-09-25 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Stuart A. Rice
Publisher : John Wiley & Sons
ISBN 13 : 1119325552
Total Pages : 410 pages
Book Rating : 4.1/5 (193 download)

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Book Synopsis Advances in Chemical Physics, Volume 162 by : Stuart A. Rice

Download or read book Advances in Chemical Physics, Volume 162 written by Stuart A. Rice and published by John Wiley & Sons. This book was released on 2017-08-17 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Andres M. Kowalski, Raul D. Rossignoli and Evaldo M. F. Curado
Publisher : Bentham Science Publishers
ISBN 13 : 1608057607
Total Pages : 432 pages
Book Rating : 4.6/5 (8 download)

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Book Synopsis Concepts and Recent Advances in Generalized Information Measures and Statistics by : Andres M. Kowalski, Raul D. Rossignoli and Evaldo M. F. Curado

Download or read book Concepts and Recent Advances in Generalized Information Measures and Statistics written by Andres M. Kowalski, Raul D. Rossignoli and Evaldo M. F. Curado and published by Bentham Science Publishers. This book was released on 2013-12-13 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Fixed Point Theory and Fractional Calculus

Author : Pradip Debnath
Publisher : Springer Nature
ISBN 13 : 9811906688
Total Pages : 358 pages
Book Rating : 4.8/5 (119 download)

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Book Synopsis Fixed Point Theory and Fractional Calculus by : Pradip Debnath

Download or read book Fixed Point Theory and Fractional Calculus written by Pradip Debnath and published by Springer Nature. This book was released on 2022-05-10 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects chapters on fixed-point theory and fractional calculus and their applications in science and engineering. It discusses state-of-the-art developments in these two areas through original new contributions from scientists across the world. It contains several useful tools and techniques to develop their skills and expertise in fixed-point theory and fractional calculus. New research directions are also indicated in chapters. This book is meant for graduate students and researchers willing to expand their knowledge in these areas. The minimum prerequisite for readers is the graduate-level knowledge of analysis, topology and functional analysis.

Special Functions: Fractional Calculus and the Pathway for Entropy

Author : Hans J. Haubold
Publisher : MDPI
ISBN 13 : 3038426652
Total Pages : 305 pages
Book Rating : 4.0/5 (384 download)

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Book Synopsis Special Functions: Fractional Calculus and the Pathway for Entropy by : Hans J. Haubold

Download or read book Special Functions: Fractional Calculus and the Pathway for Entropy written by Hans J. Haubold and published by MDPI. This book was released on 2018-03-23 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a printed edition of the Special Issue "Special Functions: Fractional Calculus and the Pathway for Entropy Dedicated to Professor Dr. A.M. Mathai on the occasion of his 80th Birthday" that was published in Axioms

Time Series Analysis in Seismology

Author : Alejandro Ramírez-Rojas
Publisher : Elsevier
ISBN 13 : 0128149027
Total Pages : 406 pages
Book Rating : 4.1/5 (281 download)

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Book Synopsis Time Series Analysis in Seismology by : Alejandro Ramírez-Rojas

Download or read book Time Series Analysis in Seismology written by Alejandro Ramírez-Rojas and published by Elsevier. This book was released on 2019-08-02 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: Time Series Analysis in Seismology: Practical Applications provides technical assistance and coverage of available methods to professionals working in the field of seismology. Beginning with a thorough review of open problems in geophysics, including tectonic plate dynamics, localization of solitons, and forecasting, the book goes on to describe the various types of time series or punctual processes obtained from those systems. Additionally, the book describes a variety of methods and techniques relating to seismology and includes a discussion of future developments and improvements. Time Series Analysis in Seismology offers a concise presentation of the most recent advances in the analysis of geophysical data, particularly with regard to seismology, making it a valuable tool for researchers and students working in seismology and geophysics. Presents the necessary tools for time series analysis as it relates to seismology in a compact and consistent manner Includes a discussion of technical resources that can be applied to time series data analysis across multiple disciplines Describes the methods and techniques available for solving problems related to the analysis of complex data sets Provides exercises at the end of each chapter to enhance comprehension