A self-contained, mathematical introduction to the driving ideas in equilibrium statistical mechanics, studying important models in detail.

This book provides a comprehensive exposition of the theory of equilibrium thermodynamics and statistical mechanics at a level suitable for well-prepared undergraduate students. The fundamental message of the book is that all results in equilibrium thermodynamics and statistical mechanics follow from a single unprovable axiom — namely, the principle of equal a priori probabilities — combined with elementary probability theory, elementary classical mechanics, and elementary quantum mechanics.

This comprehensive work provides a rigorous introduction to statistical mechanics, which aims to relate microscopic properties of matter to observed macroscopic, or bulk, behavior of physical systems. The foundations of statistical mechanics, laid down by Gibbs, are presented in detail along with an introductory chapter on thermodynamics. Other topics covered include model systems and the thermodynamic limit; theories of phase transitions; fluctuations and correlations; exactly solved models; scaling theory; and the renormalization group. An important feature of the book is many problems and worked solutions which provide a timely demonstration of current research activity in the field.

Statistical mechanics deals with systems in which chaos and randomness reign supreme. The current theory is therefore firmly based on the equations of classical mechanics and the postulates of probability theory. This volume seeks to present a unified account of classical mechanical statistics, rather than a collection of unconnected reviews on recent results. To help achieve this, one element is emphasised which integrates various parts of the prevailing theory into a coherent whole. This is the hierarchy of the BBGKY equations, which enables a relationship to be established between the Gibbs theory, the liquid theory, and the theory of nonequilibrium phenomena. As the main focus is on the complex theoretical subject matter, attention to applications is kept to a minimum. The book is divided into three parts. The first part describes the fundamentals of the theory, embracing chaos in dynamic systems and distribution functions of dynamic systems. Thermodynamic equilibrium, dealing with Gibbs statistical mechanics and the statistical mechanics of liquids, forms the second part. Lastly, the third part concentrates on kinetics, and the theory of nonequilibrium gases and liquids in particular. Audience: This book will be of interest to graduate students and researchers whose work involves thermophysics, theory of surface phenomena, theory of chemical reactions, physical chemistry and biophysics.

This textbook facilitates students’ ability to apply fundamental principles and concepts in classical thermodynamics to solve challenging problems relevant to industry and everyday life. It also introduces the reader to the fundamentals of statistical mechanics, including understanding how the microscopic properties of atoms and molecules, and their associated intermolecular interactions, can be accounted for to calculate various average properties of macroscopic systems. The author emphasizes application of the fundamental principles outlined above to the calculation of a variety of thermodynamic properties, to the estimation of conversion efficiencies for work production by heat interactions, and to the solution of practical thermodynamic problems related to the behavior of non-ideal pure fluids and fluid mixtures, including phase equilibria and chemical reaction equilibria. The book contains detailed solutions to many challenging sample problems in classical thermodynamics and statistical mechanics that will help the reader crystallize the material taught. Class-tested and perfected over 30 years of use by nine-time Best Teaching Award recipient Professor Daniel Blankschtein of the Department of Chemical Engineering at MIT, the book is ideal for students of Chemical and Mechanical Engineering, Chemistry, and Materials Science, who will benefit greatly from in-depth discussions and pedagogical explanations of key concepts. Distills critical concepts, methods, and applications from leading full-length textbooks, along with the author’s own deep understanding of the material taught, into a concise yet rigorous graduate and advanced undergraduate text; Enriches the standard curriculum with succinct, problem-based learning strategies derived from the content of 50 lectures given over the years in the Department of Chemical Engineering at MIT; Reinforces concepts covered with detailed solutions to illuminating and challenging homework problems.

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.

This book provides a rapid overview of the basic methods and concepts in mechanics for beginning Ph.D. students and advanced undergraduates in applied mathematics or related fields. It is based on a graduate course given in 2006-07 at the Courant Institute of Mathematical Sciences. Among other topics, the book introduces Newton's law, action principles, Hamilton-Jacobi theory, geometric wave theory, analytical and numerical statistical mechanics, discrete and continuous quantum mechanics, and quantum path-integral methods. The focus is on fundamental mathematical methods that provide connections between seemingly unrelated subjects. An example is Hamilton-Jacobi theory, which appears in the calculus of variations, in Fermat's principle of classical mechanics, and in the geometric theory of dispersive wavetrains. The material is developed in a sequence of simple examples and the book can be used in a one-semester class on classical, statistical, and quantum mechanics. Some familiarity with differential equations is required but otherwise the book is self-contained. In particular, no previous knowledge of physics is assumed. Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.

Statistical Mechanics discusses the fundamental concepts involved in understanding the physical properties of matter in bulk on the basis of the dynamical behavior of its microscopic constituents. The book emphasizes the equilibrium states of physical systems. The text first details the statistical basis of thermodynamics, and then proceeds to discussing the elements of ensemble theory. The next two chapters cover the canonical and grand canonical ensemble. Chapter 5 deals with the formulation of quantum statistics, while Chapter 6 talks about the theory of simple gases. Chapters 7 and 8 examine the ideal Bose and Fermi systems. In the next three chapters, the book covers the statistical mechanics of interacting systems, which includes the method of cluster expansions, pseudopotentials, and quantized fields. Chapter 12 discusses the theory of phase transitions, while Chapter 13 discusses fluctuations. The book will be of great use to researchers and practitioners from wide array of disciplines, such as physics, chemistry, and engineering.

From the reviews: "This book excels by its variety of modern examples in solid state physics, magnetism, elementary particle physics [...] I can recommend it strongly as a valuable source, especially to those who are teaching basic statistical physics at our universities." Physicalia

This is the definitive treatise on the fundamentals of statistical mechanics. A concise exposition of classical statistical mechanics is followed by a thorough elucidation of quantum statistical mechanics: postulates, theorems, statistical ensembles, changes in quantum mechanical systems with time, and more. The final two chapters discuss applications of statistical mechanics to thermodynamic behavior. 1930 edition.