Mathematical Foundations of Statistical Mechanics PDF Download
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Author: Aleksandr I?Akovlevich Khinchin
Publisher: Courier Corporation
ISBN: 9780486601472
Category : Mathematics
Languages : en
Pages : 212
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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.
Author: Aleksandr I?Akovlevich Khinchin
Publisher: Courier Corporation
ISBN: 9780486601472
Category : Mathematics
Languages : en
Pages : 212
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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.
Author: John von Neumann
Publisher: Princeton University Press
ISBN: 9780691028934
Category : Mathematics
Languages : en
Pages : 462
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Book Description
A revolutionary book that for the first time provided a rigorous mathematical framework for quantum mechanics. -- Google books
Author: D.Y. Petrina
Publisher: Springer Science & Business Media
ISBN: 940110185X
Category : Science
Languages : en
Pages : 460
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Book Description
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: Jean-Bernard Bru
Publisher: Springer Nature
ISBN: 3031289498
Category : Science
Languages : en
Pages : 497
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Book Description
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: Robert H. Swendsen
Publisher: Oxford University Press
ISBN: 0199646945
Category : Mathematics
Languages : en
Pages : 422
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Book Description
This text presents statistical mechanics and thermodynamics as a theoretically integrated field of study. It stresses deep coverage of fundamentals, providing a natural foundation for advanced topics. The large problem sets (with solutions for teachers) include many computational problems to advance student understanding.
Author: Library of Congress. Copyright Office
Publisher:
ISBN:
Category : American literature
Languages : en
Pages : 1142
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Book Description
Author: Sacha Friedli
Publisher: Cambridge University Press
ISBN: 1107184827
Category : Mathematics
Languages : en
Pages : 643
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Book Description
A self-contained, mathematical introduction to the driving ideas in equilibrium statistical mechanics, studying important models in detail.
Author:
Publisher:
ISBN:
Category : Great Britain
Languages : en
Pages : 1668
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Book Description
Author: John T. Roberts
Publisher: OUP Oxford
ISBN: 0191565318
Category : Philosophy
Languages : en
Pages : 421
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Book Description
John T. Roberts presents and defends a radically new theory of laws of nature, the Measurability Account. Though consistent with a Humean ontology, Roberts's theory differs sharply from the most influential Humean theory of laws, David Lewis's Best-System Analysis. Unlike other Humean theories, the Measurability Account affirms that there is an important sense in which the laws govern the universe, rather than simply describing it economically. Yet unlike non-Humean theories, it requires only minimal metaphysical commitments. In this way, it combines the advantages of Humean and non-Humean approaches to laws, while avoiding the pitfalls of each. At the heart of the Measurability Account are two new ideas: that lawhood is not a property of facts but rather a role that a proposition can play within a scientific theory, and that what is essential to laws is that they guarantee the reliability of methods of measuring natural quantities. On the basis of these ideas, Roberts argues that we can offer an informative and compelling explanation of why laws have the peculiar counterfactual resilience that sets them apart from accidental uniformities.
Author: R. Jancel
Publisher: Elsevier
ISBN: 1483186261
Category : Science
Languages : en
Pages : 441
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Book Description
Foundations of Classical and Quantum Statistical Mechanics details the theoretical foundation the supports the concepts in classical and quantum statistical mechanics. The title discusses the various problems set by the theoretical justification of statistical mechanics methods. The text first covers the the ergodic theory in classical statistical mechanics, and then proceeds to tackling quantum mechanical ensembles. Next, the selection discusses the the ergodic theorem in quantum statistical mechanics and probability quantum ergodic theorems. The selection also details H-theorems and kinetic equations in classical and quantum statistical mechanics. The book will be of great interest to students, researchers, and practitioners of physics, chemistry, and engineering.
