Mathematical Foundations of Statistical Mechanics

Author: Aleksandr I?Akovlevich Khinchin
Publisher: Courier Corporation
ISBN: 0486601471
Category : Mathematics
Languages : en
Pages : 210

Book Description
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.

Foundations of Statistical Mechanics

Author: O. Penrose
Publisher: Elsevier
ISBN: 1483156486
Category : Science
Languages : en
Pages : 272

Book Description
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.

Mathematical Foundations of Classical Statistical Mechanics

Author: D.Ya. Petrina
Publisher: CRC Press
ISBN: 9780415273541
Category : Science
Languages : en
Pages : 352

Book Description
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.

Mathematical Foundations of Quantum Mechanics

Author: John von Neumann
Publisher: Princeton University Press
ISBN: 9780691028934
Category : Mathematics
Languages : en
Pages : 462

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

The Conceptual Foundations of the Statistical Approach in Mechanics

Author: Paul Ehrenfest
Publisher: Courier Corporation
ISBN: 0486163148
Category : Science
Languages : en
Pages : 128

Book Description
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.

Mathematical Foundations of Information Theory

Author: Aleksandr I?Akovlevich Khinchin
Publisher: Courier Corporation
ISBN: 0486604349
Category : Mathematics
Languages : en
Pages : 130

Book Description
First comprehensive introduction to information theory explores the work of Shannon, McMillan, Feinstein, and Khinchin. Topics include the entropy concept in probability theory, fundamental theorems, and other subjects. 1957 edition.

Mathematical Foundations of Quantum Statistics

Author: Aleksandr I︠A︡kovlevich Khinchin
Publisher:
ISBN:
Category : Science
Languages : en
Pages : 252

Book Description

Foundations of Statistical Mechanics

Author: W.T. Grandy Jr.
Publisher: Springer Science & Business Media
ISBN: 9400938675
Category : Science
Languages : en
Pages : 391

Book Description
In a certain sense this book has been twenty-five years in the writing, since I first struggled with the foundations of the subject as a graduate student. It has taken that long to develop a deep appreciation of what Gibbs was attempting to convey to us near the end of his life and to understand fully the same ideas as resurrected by E.T. Jaynes much later. Many classes of students were destined to help me sharpen these thoughts before I finally felt confident that, for me at least, the foundations of the subject had been clarified sufficiently. More than anything, this work strives to address the following questions: What is statistical mechanics? Why is this approach so extraordinarily effective in describing bulk matter in terms of its constituents? The response given here is in the form of a very definite point of view-the principle of maximum entropy (PME). There have been earlier attempts to approach the subject in this way, to be sure, reflected in the books by Tribus [Thermostat ics and Thermodynamics, Van Nostrand, 1961], Baierlein [Atoms and Information Theory, Freeman, 1971], and Hobson [Concepts in Statistical Mechanics, Gordon and Breach, 1971].

Statistical Mechanics

Author: Giovanni Gallavotti
Publisher: Springer Science & Business Media
ISBN: 3662039524
Category : Science
Languages : en
Pages : 344

Book Description
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.

The Road to Maxwell's Demon

Author: Meir Hemmo
Publisher: Cambridge University Press
ISBN: 1107019680
Category : Science
Languages : en
Pages : 341

Book Description
A philosophical perspective to statistical mechanics for graduate students and researchers in the foundations and philosophy of physics.