Download or read book Mathematical Foundations of Statistical Mechanics written by Aleksandr I︠A︡kovlevich Khinchin and published by Dover Books on Mathematics. This book was released on 1949-06 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: The translation of this important book brings to the English-speaking mathematician and mathematical physicist a thoroughly up-to-date introduction to statistical mechanics. It offers a precise and mathematically rigorous formulation of the problems of statistical mechanics, as opposed to the non-rigorous discussion presented in most other works. It provides analytical tools needed to replace many of the cumbersome concepts and devices commonly used for establishing basic formulae, and it furnishes the mathematician with a logical step-by-step introduction, which will enable him to master the elements of statistical mechanics in the shortest possible time. After a historical sketch, the author discusses the geometry and kinematics of the phase space, with the theorems of Liouville and Birkhoff; the ergodic problem (in the sense of replacing time averages by phase averages); the theory of probability; central limit theorem; ideal monatomic gas; foundation of thermodynamics, and dispersion and distribution of sum functions. "An excellent introduction to the difficult and important discipline of Statistical Mechanics. It is clear, concise, and rigorous. There is a very good chapter on the ergodic theorem (with a complete proof!) and . . . a highly lucid chapter on statistical foundations of thermodynamics . . . useful to teachers . . . and to mathematicians." ― M. Kac, Quarterly of Applied Mathematics.

Download or read book Mathematical foundations of statistical mechanics tr written by Aleksandr I︠A︡kovlevich Khinchin and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Mathematical Foundations of Classical Statistical Mechanics written by D.Ya. Petrina and published by CRC Press. This book was released on 2002-04-11 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph considers systems of infinite number of particles, in particular the justification of the procedure of thermodynamic limit transition. The authors discuss the equilibrium and non-equilibrium states of infinite classical statistical systems. Those states are defined in terms of stationary and nonstationary solutions to the Bogolyubov

Download or read book Mathematical Foundations of Statistical Mechanics written by Aleksandr I︠A︡kovlevich Khinchin and published by . This book was released on 1964 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Mathematical Foundations of Classical Statistical Mechanics written by D.Ya. Petrina and published by CRC Press. This book was released on 2002-04-11 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph considers systems of infinite number of particles, in particular the justification of the procedure of thermodynamic limit transition. The authors discuss the equilibrium and non-equilibrium states of infinite classical statistical systems. Those states are defined in terms of stationary and nonstationary solutions to the Bogolyubov equations for the sequences of correlation functions in the thermodynamic limit. This is the first detailed investigation of the thermodynamic limit for non-equilibrium systems and of the states of infinite systems in the cases of both canonical and grand canonical ensembles, for which the thermodynamic equivalence is proved. A comprehensive survey of results is also included; it concerns the properties of correlation functions for infinite systems and the corresponding equations. For this new edition, the authors have made changes to reflect the development of theory in the last ten years. They have also simplified certain sections, presenting them more systematically, and greatly increased the number of references. The book is aimed at theoretical physicists and mathematicians and will also be of use to students and postgraduate students in the field.

Download or read book Mathematical Foundations of Statistical Mechanics written by A. Khinchin and published by . This book was released on 2014-06-08 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: 2014 Reprint of 1949 Edition. Full facsimile of the original edition, not reproduced with Optical Recognition Software. The translation of this important work brings to the American mathematician and physicist a useful work of statistical mechanics. It offers a precise and mathematically satisfactory formulation of the problems of statistical mechanics and provides the analytic tools needed to replace many of the cumbersome concepts and devices commonly found in more basic works on the subject. And above all, it furnishes the mathematician approaching the subject for the first time with a logical, step-by-step introduction, written in mathematical terms, to aid in mastering the subject in the shortest possible time. Contents 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. -- Dispersion and the distributions of sum functions. Aleksandr Khinchin was a Soviet mathematician and one of the most significant people in the Soviet school of probability theory.

Download or read book Mathematical Foundations of Statistical Mechanics written by A. Ya. Khinchin and published by Courier Corporation. This book was released on 2013-01-17 with total page 244 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; Reduction to the Problem of the Theory of Probability; and more.

Download or read book Mathematical Foundations of Quantum Statistical Mechanics written by D.Y. Petrina and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is devoted to quantum statistical mechanics. It can be regarded as a continuation of the book "Mathematical Foundations of Classical Statistical Mechanics. Continuous Systems" (Gordon & Breach SP, 1989) written together with my colleagues V. I. Gerasimenko and P. V. Malyshev. Taken together, these books give a complete pre sentation of the statistical mechanics of continuous systems, both quantum and classical, from the common point of view. Both books have similar contents. They deal with the investigation of states of in finite systems, which are described by infinite sequences of statistical operators (reduced density matrices) or Green's functions in the quantum case and by infinite sequences of distribution functions in the classical case. The equations of state and their solutions are the main object of investigation in these books. For infinite systems, the solutions of the equations of state are constructed by using the thermodynamic limit procedure, accord ing to which we first find a solution for a system of finitely many particles and then let the number of particles and the volume of a region tend to infinity keeping the density of particles constant. However, the style of presentation in these books is quite different.

Download or read book Elementary Principles in Statistical Mechanics written by J. Willard Gibbs and published by Courier Corporation. This book was released on 2014-12-17 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: First book to unite the works of Clausius, Maxwell, Boltzmann, and the author himself. Gibbs' lucid advanced-level text remains a valuable collection of fundamental equations and principles. 1902 edition.

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 Statistical Mechanics An Intermediate Course 2nd Edition written by Elisa Ercolessi and published by World Scientific Publishing Company. This book was released on 2001-05-17 with total page 668 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers the foundations of classical thermodynamics, with emphasis on the use of differential forms of classical and quantum statistical mechanics, and also on the foundational aspects. In both contexts, a number of applications are considered in detail, such as the general theory of response, correlations and fluctuations, and classical and quantum spin systems. In the quantum case, a self-contained introduction to path integral methods is given. In addition, the book discusses phase transitions and critical phenomena, with applications to the Landau theory and to the Ginzburg-Landau theory of superconductivity, and also to the phenomenon of Bose condensation and of superfluidity. Finally, there is a careful discussion on the use of the renormalization group in the study of critical phenomena.

Download or read book Foundations of Statistical Mechanics written by O. Penrose and published by Elsevier. This book was released on 2016-09-21 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: International Series of Monographs in Natural Philosophy, Volume 22: Foundations of Statistical Mechanics: A Deductive Treatment presents the main approaches to the basic problems of statistical mechanics. This book examines the theory that provides explicit recognition to the limitations on one's powers of observation. Organized into six chapters, this volume begins with an overview of the main physical assumptions and their idealization in the form of postulates. This text then examines the consequences of these postulates that culminate in a derivation of the fundamental formula for calculating probabilities in terms of dynamic quantities. Other chapters provide a careful analysis of the significant notion of entropy, which shows the links between thermodynamics and statistical mechanics and also between communication theory and statistical mechanics. The final chapter deals with the thermodynamic concept of entropy. This book is intended to be suitable for students of theoretical physics. Probability theorists, statisticians, and philosophers will also find this book useful.

Download or read book Mathematical foundations of statistical mechanics written by Aleksandr Ja Chinčin and published by . This book was released on 1949 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Mathematical Foundations of Statistical Mechanics written by K. K. Tiwari (College principal) and published by . This book was released on 2019 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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

Download or read book Statistical Mechanics Made Simple written by Daniel Charles Mattis and published by World Scientific. This book was released on 2003 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elementary concepts in statistics and probability - The ising model and the lattice gas - Elements of thermodynamics - Statistical mechanics - The world of bosons - All about fermions : theories of metals, superconductors, semiconductors - Kinetic theory - The transfer matrix - Some uses of quantum field theory in statistical physics.

Download or read book Mathematical Foundations of Statistical Mechanics written by A. I. Khinchin and published by . This book was released on 1975 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: