Mathematical Foundations Of Classical Statistical Mechanics

Author : D.Ya. Petrina,V.I. Gerasimenko,P V Malyshev
Publisher : CRC Press
Page : 352 pages
File Size : 47,5 Mb
Release : 2002-04-11
Category : Science
ISBN : 0415273544

Get Book

Mathematical Foundations of Classical Statistical Mechanics by D.Ya. Petrina,V.I. Gerasimenko,P V Malyshev Pdf

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.

Author : D.Ya. Petrina,V.I. Gerasimenko,P V Malyshev
Publisher : CRC Press
Page : 352 pages
File Size : 53,6 Mb
Release : 2002-04-11
Category : Mathematics
ISBN : 9781482265026

Get Book

Mathematical Foundations of Classical Statistical Mechanics by D.Ya. Petrina,V.I. Gerasimenko,P V Malyshev Pdf

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

Author : Aleksandr I?Akovlevich Khinchin
Publisher : Courier Corporation
Page : 210 pages
File Size : 55,9 Mb
Release : 1949-01-01
Category : Mathematics
ISBN : 9780486601472

Get Book

Mathematical Foundations of Statistical Mechanics by Aleksandr I?Akovlevich Khinchin Pdf

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.

Author : D.Y. Petrina
Publisher : Springer Science & Business Media
Page : 460 pages
File Size : 40,7 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789401101851

Get Book

Mathematical Foundations of Quantum Statistical Mechanics by D.Y. Petrina Pdf

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.

Author : A. Ya. Khinchin
Publisher : Courier Corporation
Page : 244 pages
File Size : 51,5 Mb
Release : 2013-01-17
Category : Mathematics
ISBN : 9780486138732

Get Book

Mathematical Foundations of Statistical Mechanics by A. Ya. Khinchin Pdf

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.

Author : Sabir Umarov,Tsallis Constantino
Publisher : World Scientific
Page : 336 pages
File Size : 51,6 Mb
Release : 2022-03-03
Category : Science
ISBN : 9789811245176

Get Book

Mathematical Foundations Of Nonextensive Statistical Mechanics by Sabir Umarov,Tsallis Constantino Pdf

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.

Author : Dmitriĭ I͡Akovlevich Petrina,Viktor Ivanovich Gerasimenko,Petr Vitalʹevich Malyshev
Publisher : CRC Press
Page : 362 pages
File Size : 45,6 Mb
Release : 1989
Category : Mathematical physics
ISBN : 2881246818

Get Book

Mathematical Foundations of Classical Statistical Mechanics by Dmitriĭ I͡Akovlevich Petrina,Viktor Ivanovich Gerasimenko,Petr Vitalʹevich Malyshev Pdf

Introducing the functional method practiced in the USSR, this well- translated monograph considers the problem of investigating systems of infinite numbers of particles. It discusses the equilibrium and non- equilibrium states of infinite classical statistical systems, and investigates the thermodynamic limit for non-equilibrium systems and of the states of infinite systems, for which thermodynamic equivalence is proved. Book club price, $95. Annotation copyrighted by Book News, Inc., Portland, OR

Author : Véronique Gayrard,Louis-Pierre Arguin,Nicola Kistler,Irina Kourkova
Publisher : Springer Nature
Page : 279 pages
File Size : 54,8 Mb
Release : 2019-09-15
Category : Mathematics
ISBN : 9783030290771

Get Book

Statistical Mechanics of Classical and Disordered Systems by Véronique Gayrard,Louis-Pierre Arguin,Nicola Kistler,Irina Kourkova Pdf

These proceedings of the conference Advances in Statistical Mechanics, held in Marseille, France, August 2018, focus on fundamental issues of equilibrium and non-equilibrium dynamics for classical mechanical systems, as well as on open problems in statistical mechanics related to probability, mathematical physics, computer science, and biology. Statistical mechanics, as envisioned more than a century ago by Boltzmann, Maxwell and Gibbs, has recently undergone stunning twists and developments which have turned this old discipline into one of the most active areas of truly interdisciplinary and cutting-edge research. The contributions to this volume, with their rather unique blend of rigorous mathematics and applications, outline the state-of-the-art of this success story in key subject areas of equilibrium and non-equilibrium classical and quantum statistical mechanics of both disordered and non-disordered systems. Aimed at researchers in the broad field of applied modern probability theory, this book, and in particular the review articles, will also be of interest to graduate students looking for a gentle introduction to active topics of current research.

Author : Jean-Bernard Bru,Walter Alberto de Siqueira Pedra
Publisher : Springer Nature
Page : 497 pages
File Size : 46,6 Mb
Release : 2023-06-16
Category : Science
ISBN : 9783031289491

Get Book

C*-Algebras and Mathematical Foundations of Quantum Statistical Mechanics by Jean-Bernard Bru,Walter Alberto de Siqueira Pedra Pdf

This textbook provides a comprehensive introduction to the mathematical foundations of quantum statistical physics. It presents a conceptually profound yet technically accessible path to the C*-algebraic approach to quantum statistical mechanics, demonstrating how key aspects of thermodynamic equilibrium can be derived as simple corollaries of classical results in convex analysis. Using C*-algebras as examples of ordered vector spaces, this book makes various aspects of C*-algebras and their applications to the mathematical foundations of quantum theory much clearer from both mathematical and physical perspectives. It begins with the simple case of Gibbs states on matrix algebras and gradually progresses to a more general setting that considers the thermodynamic equilibrium of infinitely extended quantum systems. The book also illustrates how first-order phase transitions and spontaneous symmetry breaking can occur, in contrast to the finite-dimensional situation. One of the unique features of this book is its thorough and clear treatment of the theory of equilibrium states of quantum mean-field models. This work is self-contained and requires only a modest background in analysis, topology, and functional analysis from the reader. It is suitable for both mathematicians and physicists with a specific interest in quantum statistical physics.

Author : Giovanni Gallavotti
Publisher : Springer Science & Business Media
Page : 344 pages
File Size : 50,5 Mb
Release : 2013-11-11
Category : Science
ISBN : 9783662039526

Get Book

Statistical Mechanics by Giovanni Gallavotti Pdf

This clear book presents a critical and modern analysis of the conceptual foundations of statistical mechanics as laid down in Boltzmann's works. The author emphasises the relation between microscopic reversibility and macroscopic irreversibility, explaining fundamental concepts in detail.

Author : A. Khinchin
Publisher : Unknown
Page : 188 pages
File Size : 46,8 Mb
Release : 2014-06-08
Category : Science
ISBN : 1614276420

Get Book

Mathematical Foundations of Statistical Mechanics by A. Khinchin Pdf

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.

Author : Oliver Bühler
Publisher : American Mathematical Soc.
Page : 178 pages
File Size : 48,6 Mb
Release : 2006
Category : Mathematics
ISBN : 0821883534

Get Book

A Brief Introduction to Classical, Statistical, and Quantum Mechanics by Oliver Bühler Pdf

Author : A. Y. Khinchin
Publisher : Courier Corporation
Page : 256 pages
File Size : 43,5 Mb
Release : 2013-02-21
Category : Mathematics
ISBN : 9780486167657

Get Book

Mathematical Foundations of Quantum Statistics by A. Y. Khinchin Pdf

A coherent, well-organized look at the basis of quantum statistics’ computational methods, the determination of the mean values of occupation numbers, the foundations of the statistics of photons and material particles, thermodynamics.

Author : Colin J. Thompson
Publisher : Princeton University Press
Page : 289 pages
File Size : 50,9 Mb
Release : 2015-03-08
Category : Science
ISBN : 9781400868681

Get Book

Mathematical Statistical Mechanics by Colin J. Thompson Pdf

While most introductions to statistical mechanics are either too mathematical or too physical, Colin Thompson's book combines mathematical rigor with familiar physical materials. Following introductory chapters on kinetic theory, thermodynamics, the Gibbs ensembles, and the thermodynamic limit, later chapters discuss the classical theories of phase transitions, the Ising model, algebraic methods and combinatorial methods for solving the two-dimensional model in zero field, and some applications of the Ising model to biology. Originally published in 1979. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Author : John von Neumann
Publisher : Princeton University Press
Page : 462 pages
File Size : 46,5 Mb
Release : 1955
Category : Mathematics
ISBN : 0691028931

Get Book

Mathematical Foundations of Quantum Mechanics by John von Neumann Pdf

A revolutionary book that for the first time provided a rigorous mathematical framework for quantum mechanics. -- Google books