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The science of statistical mechanics is concerned with defining the thermodynamic properties of a macroscopic sample in terms of the properties of the microscopic systems of which it is composed. The aim of this book is to provide a clear, logical, and self-contained treatment of equilibrium statistical mechanics starting from Boltzmann's two statistical assumptions, and to present a wide variety of applications to diverse physical assemblies. The coverage is enhanced and extended through an extensive set of accessible problems. An appendix provides an introduction to non-equilibrium statistical mechanics through the Boltzmann equation and its extensions. The book assumes introductory courses in classical and quantum mechanics, as well as familiarity with multi-variable calculus and the essentials of complex analysis. Some knowledge of thermodynamics is assumed, although the book starts with an appropriate review of that topic. The targeted audience is first-year graduate students, and advanced undergraduates, in physics, chemistry, and the related physical sciences. The goal of this text is to help the reader obtain a clear working knowledge of the very useful and powerful methods of equilibrium statistical mechanics and to enhance the understanding and appreciation of the more advanced texts.
Sample Chapter(s)
Table of Contents (731 KB)
Chapter 1: Introduction (254 KB)
Chapter 2: The Microcanonical Ensemble (385 KB)
Chapter 3: Applications of the Microcanonical Ensemble (495 KB)
Contents:
- Introduction:
- Review of Thermodynamics
- Basic Statistical Hypotheses
- The Microcanonical Ensemble:
- Independent Localized Systems
- The Boltzmann Distribution
- The Partition Function
- Method of Steepest Descent
- Independent Non-Localized Systems
- Transition to Classical Dynamics
- Applications of the Microcanonical Ensemble:
- Internal Partition Function
- Molecular Spectroscopy
- Paramagnetic and Dielectric Assemblies
- Chemical Equilibria
- The Canonical Ensemble:
- Constant-Temperature Partition Function
- Classical Limit
- Energy Distribution
- Summary of Results So Far
- Applications of the Canonical Ensemble:
- Solids
- Imperfect Gases
- The Grand Canonical Ensemble:
- Grand Partition Function
- Relation to Previous Results
- Fluctuations
- Applications of the Grand Canonical Ensemble:
- Boltzmann Statistics
- Quantum Statistics
- Bosons
- Fermions
- Special Topics:
- Solutions
- Order-Disorder Transitions in Crystals
- The Ising Model
- Lattice Gauge Theory
- Problems
Readership: Advanced undergraduates, beginning graduate students in physics, chemistry and related physical sciences.
