Statistical Mechanics Made Simple

This book is an elaboration of the author's lecture notes in a graduate course in thermodynamics and statistical mechanics. The original notes supplemented topics lacking in traditional texts. In its present augmented version the book may be used as the sole or primary text in a one-semester course in thermodynamics/statistical mechanics or as an adjunct text in a two-semester course.

Statistical mechanics is the application of physics or chemistry at finite temperature T and can encompass as many topics involving these disciplines as one wishes. As much as the quality of presentation, it is the choice of topics that distinguishes from one another the scores of textbooks with the word "statistical" or "statistics" in the title. The present book is intended to respond to the curiosity of the reader about fundamental principles. It shows in detail how one solves the problems that arise in connection with these principles. There are some 50 problems scattered throughout the text and a similar number of illustrations. All the mathematics is self-contained, includ

Preface	p. ix
Introduction: Theories of Thermodynamics, Kinetic Theory and Statistical Mechanics	p. xiii
Elementary Concepts in Statistics and Probability	p. 1
The Binomial Distribution	p. 1
Length of a Winning Streak	p. 3
Brownian Motion and the Random Walk	p. 4
Poisson versus Normal (Gaussian) Distributions	p. 5
Central Limit Theorem (CLT)	p. 9
Multinomial Distributions, Statistical Thermodynamics	p. 12
The Barometer Equation	p. 14
Other Distributions	p. 14
The Ising Model and the Lattice Gas	p. 17
Some Background and Motivation	p. 17
First-Principles Statistical Theory of Paramagnetism	p. 18
More on Entropy and Energy	p. 21
Some Other Relevant Thermodynamic Functions	p. 21
Mean-Field Theory, Stable and Metastable Solutions	p. 23
The Lattice Gas	p. 26
The Nearest-Neighbor Chain: Thermodynamics in 1D	p. 26
The Disordered Ising Chain	p. 28
Other Magnetic Systems in One Dimension	p. 28
Elements of Thermodynamics	p. 31
The Scope of Thermodynamics	p. 31
Equations of State and Some Definitions	p. 32
Maxwell Relations	p. 35
Three Important Laws of Thermodynamics	p. 35
The Second Derivatives of the Free Energy	p. 38
Phase Diagrams for the van der Waals Gas	p. 39
Clausius-Clapeyron Equation	p. 43
Phase Transitions	p. 46
The Carnot Cycle	p. 49
Superconductivity	p. 51
Statistical Mechanics	p. 55
The Formalism--and a False Start	p. 55
Gibbs' Paradox and Its Remedy	p. 58
The Gibbs Factor	p. 59
The Grand Ensemble	p. 60
Non-Ideal Gas and the 2-Body Correlation Function	p. 62
The Virial Equation of State	p. 64
Weakly Non-Ideal Gas	p. 65
Two-body Correlations	p. 68
Configurational Partition Function in 1D	p. 73
One Dimension versus Two	p. 75
Two Dimensions versus Three: The Debye-Waller Factors	p. 77
The World of Bosons	p. 83
Two Types of Bosons and Their Operators	p. 83
Number Representation and the Many-Body Problem	p. 86
The Adiabatic Process and Conservation of Entropy	p. 88
Many-Body Perturbations	p. 89
Photons	p. 90
Phonons	p. 93
Ferromagnons	p. 96
Conserved Bosons and the Ideal Bose Gas	p. 99
Nature of "Ideal" Bose-Einstein Condensation	p. 101
Ideal Bose-Einstein Condensation in Low Dimensions	p. 104
Consequences of a Hard Core Repulsion in 1D	p. 106
Bosons in 3D Subject to Weak Two-Body Forces	p. 109
Superfluid Helium (He II)	p. 114
All About Fermions: Theories of Metals, Superconductors, Semiconductors	p. 119
Fermi-Dirac Particles	p. 119
Slater Determinant: The Ground State	p. 120
Ideal Fermi-Dirac Gas	p. 121
Ideal Fermi-Dirac Gas with Spin	p. 123
Fermi Integrals	p. 124
Thermodynamic Functions of an Ideal Metal	p. 125
Quasiparticles and Elementary Excitations	p. 128
Semiconductor Physics: Electrons and Holes	p. 130
n-Type Semiconductor Physics: The Statistics	p. 131
Correlations and the Coulomb Repulsion	p. 132
Miscellaneous Properties of Semiconductors	p. 135
Aspects of Superconductivity: Cooper Pairs	p. 137
Aspects of BCS Theory	p. 140
Contemporary Developments in Superconductivity	p. 146
Kinetic Theory	p. 149
Scope of This Chapter	p. 149
Quasi-Equilibrium Flows and the Second Law	p. 150
The Collision Integral	p. 151
Approach to Equilibrium of a "Classical" Non-Ideal Gas	p. 154
A New Look at "Quantum Statistics"	p. 156
Master Equation: Application to Radioactive Decay	p. 158
Boltzmann Equation	p. 160
Electrical Currents in a Low-Density Electron Gas	p. 162
Diffusion and the Einstein Relation	p. 165
Electrical Conductivity of Metals	p. 165
Exactly Solved "Backscattering" Model	p. 166
Electron-Phonon Scattering	p. 169
Approximating the Boltzmann Equation	p. 170
Crossed Electric and Magnetic Fields	p. 171
Propagation of Sound Waves in Fluids	p. 173
The Calculations and Their Result	p. 178
The Transfer Matrix	p. 183
The Transfer Matrix and the Thermal Zipper	p. 183
Opening and Closing a "Zipper Ladder" or Polymer	p. 186
The Full Zipper (N [greater than sign] 2)	p. 190
The Transfer Matrix and Gaussian Potentials	p. 191
Transfer Matrix in the Ising Model	p. 192
The Ising Ladder or Polymer	p. 195
Ising Model on the Isotropic Square Lattice (2D)	p. 196
The Phase Transition	p. 201
A Question of Long-Range Order	p. 202
Ising Model in 2D and 3D	p. 204
Antiferromagnetism and Frustration	p. 206
Maximal Frustration	p. 208
Separable Model Spin-Glass without Frustration	p. 210
Critical Phenomena and Critical Exponents	p. 212
Potts Models	p. 215
Some Uses of Quantum Field Theory in Statistical Physics	p. 219
Outline of the Chapter	p. 219
Diffusion on a Lattice: Standard Formulation	p. 219
Diffusion as Expressed in QFT	p. 222
Diffusion plus One-Body Recombination Processes	p. 225
Diffusion and Two-Body Recombination Processes	p. 226
Questions Concerning Long-Range Order	p. 228
Mermin-Wagner Theorem	p. 230
Proof of Bogolubov Inequality	p. 233
Correlation Functions and the Free Energy	p. 234
Introduction to Thermodynamic Green's Functions	p. 237
Index	p. 245
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