Mathematical Foundations Of Classical Statistical Mechanics
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Author | : D.Ya. Petrina |
Publisher | : CRC Press |
Total Pages | : 352 |
Release | : 2002-04-11 |
Genre | : Science |
ISBN | : 9780415273541 |
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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 |
Publisher | : CRC Press |
Total Pages | : 352 |
Release | : 2002-04-11 |
Genre | : Mathematics |
ISBN | : 1482265028 |
Download Mathematical Foundations of Classical Statistical Mechanics Book in PDF, Epub and Kindle
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 |
Total Pages | : 210 |
Release | : 1949-01-01 |
Genre | : Mathematics |
ISBN | : 0486601471 |
Download Mathematical Foundations of Statistical Mechanics Book in PDF, Epub and Kindle
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 |
Total Pages | : 460 |
Release | : 2012-12-06 |
Genre | : Science |
ISBN | : 940110185X |
Download Mathematical Foundations of Quantum Statistical Mechanics Book in PDF, Epub and Kindle
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 | : Colin J. Thompson |
Publisher | : Princeton University Press |
Total Pages | : 289 |
Release | : 2015-03-08 |
Genre | : Science |
ISBN | : 1400868688 |
Download Mathematical Statistical Mechanics Book in PDF, Epub and Kindle
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 | : Paul Ehrenfest |
Publisher | : Courier Corporation |
Total Pages | : 128 |
Release | : 2014-11-12 |
Genre | : Science |
ISBN | : 0486163148 |
Download The Conceptual Foundations of the Statistical Approach in Mechanics Book in PDF, Epub and Kindle
Classic 1912 article reformulated the foundations of the statistical approach in mechanics. Largely still valid, the treatment covers older formulation of statistico-mechanical investigations, modern formulation of kineto-statistics of the gas model, and more. 1959 edition.
Author | : O. Penrose |
Publisher | : Elsevier |
Total Pages | : 272 |
Release | : 2016-09-21 |
Genre | : Science |
ISBN | : 1483156486 |
Download Foundations of Statistical Mechanics Book in PDF, Epub and Kindle
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.
Author | : Jean-Bernard Bru |
Publisher | : Springer Nature |
Total Pages | : 497 |
Release | : 2023-06-16 |
Genre | : Science |
ISBN | : 3031289498 |
Download C*-Algebras and Mathematical Foundations of Quantum Statistical Mechanics Book in PDF, Epub and Kindle
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 | : Sacha Friedli |
Publisher | : Cambridge University Press |
Total Pages | : 643 |
Release | : 2017-11-23 |
Genre | : Mathematics |
ISBN | : 1107184827 |
Download Statistical Mechanics of Lattice Systems Book in PDF, Epub and Kindle
A self-contained, mathematical introduction to the driving ideas in equilibrium statistical mechanics, studying important models in detail.
Author | : Aleksandr I︠A︡kovlevich Khinchin |
Publisher | : |
Total Pages | : 179 |
Release | : 1964 |
Genre | : Statistical mechanics |
ISBN | : |
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