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.

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.

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.

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.

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.

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.

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

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.

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.

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.

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.

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

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

Download or read book Optimization for Industrial Problems written by Patrick Bangert and published by Springer Science & Business Media. This book was released on 2012-01-05 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Industrial optimization lies on the crossroads between mathematics, computer science, engineering and management. This book presents these fields in interdependence as a conversation between theoretical aspects of mathematics and computer science and the mathematical field of optimization theory at a practical level. The 19 case studies that were conducted by the author in real enterprises in cooperation and co-authorship with some of the leading industrial enterprises, including RWE, Vattenfall, EDF, PetroChina, Vestolit, Sasol, and Hella, illustrate the results that may be reasonably expected from an optimization project in a commercial enterprise. The book is aimed at persons working in industrial facilities as managers or engineers; it is also suitable for university students and their professors as an illustration of how the academic material may be used in real life. It will not make its reader a mathematician but it will help its reader in improving his plant.

Download or read book ISCS 2013 Interdisciplinary Symposium on Complex Systems written by Ali Sanayei and published by Springer Science & Business Media. This book was released on 2014-02-15 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book you hold in your hands is the outcome of the "ISCS 2013: Interdisciplinary Symposium on Complex Systems" held at the historical capital of Bohemia as a continuation of our series of symposia in the science of complex systems. Prague, one of the most beautiful European cities, has its own beautiful genius loci. Here, a great number of important discoveries were made and many important scientists spent fruitful and creative years to leave unforgettable traces. The perhaps most significant period was the time of Rudolf II who was a great supporter of the art and the science and attracted a great number of prominent minds to Prague. This trend would continue. Tycho Brahe, Niels Henrik Abel, Johannes Kepler, Bernard Bolzano, August Cauchy Christian Doppler, Ernst Mach, Albert Einstein and many others followed developing fundamental mathematical and physical theories or expanding them. Thus in the beginning of the 17th century, Kepler formulated here the first two of his three laws of planetary motion on the basis of Tycho Brahe’s observations. In the 19th century, nowhere differentiable continuous functions (of a fractal character) were constructed here by Bolzano along with a treatise on infinite sets, titled “Paradoxes of Infinity” (1851). Weierstrass would later publish a similar function in 1872. In 1842, Doppler as a professor of mathematics at the Technical University of Prague here first lectured about a physical effect to bear his name later. And the epoch-making physicist Albert Einstein – while being a chaired professor of theoretical physics at the German University of Prague – arrived at the decisive steps of his later finished theory of general relativity during the years 1911–1912. In Prague, also many famous philosophers and writers accomplished their works; for instance, playwright arel ape coined the word "robot" in Prague (“robot” comes from the Czech word “robota” which means “forced labor”).

Download or read book Decoherence and Entropy in Complex Systems written by Hans-Thomas Elze and published by Springer Science & Business Media. This book was released on 2004-01-20 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: The contributions to this volume are based on selected lectures from the first international workshop on decoherence, information, complexity and entropy (DICE). The aim of this volume is to reflect the growing importance ot common concepts behind seemingly different fields such as quantum mechanics, general relativity and statistical physics in a form accessible to nonspecialist researchers. Many presentations include original results which published here for the first time.

Download or read book An Introduction to Statistical Mechanics and Thermodynamics written by Robert H. Swendsen and published by OUP Oxford. This book was released on 2012-03-01 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text presents the two complementary aspects of thermal physics as an integrated theory of the properties of matter. Conceptual understanding is promoted by thorough development of basic concepts. In contrast to many texts, statistical mechanics, including discussion of the required probability theory, is presented first. This provides a statistical foundation for the concept of entropy, which is central to thermal physics. A unique feature of the book is the development of entropy based on Boltzmann's 1877 definition; this avoids contradictions or ad hoc corrections found in other texts. Detailed fundamentals provide a natural grounding for advanced topics, such as black-body radiation and quantum gases. An extensive set of problems (solutions are available for lecturers through the OUP website), many including explicit computations, advance the core content by probing essential concepts. The text is designed for a two-semester undergraduate course but can be adapted for one-semester courses emphasizing either aspect of thermal physics. It is also suitable for graduate study.