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Tables of Contents for Statistical Mechanics
Chapter/Section Title
Page #
Page Count
PART A THERMODYNAMICS AND KINETIC THEORY
1
124
The Laws of Thermodynamics
3
28
Preliminaries
3
4
The First Law of Thermodynamics
7
2
The Second Law of Thermodynamics
9
5
Entroy
14
5
Some Immediate Consequences of the Second Law
19
3
Thermodynamic Potentials
22
3
The Third Law of Thermodynamics
25
6
Some Applications of Thermodynamics
31
21
Thermodynamic Description of Phase Transitions
31
4
Surface Effects in Condensation
35
3
Van der Waals Equation of State
38
5
Osmotic Pressure
43
5
The Limit of Thermodynamics
48
4
The Problem of Kinetic Theory
52
21
Formulation of the Problem
52
4
Binary Collisions
56
4
The Boltzmann Transport Equation
60
2
The Gibbsian Ensemble
62
3
The BBGKY Hierarchy
65
8
The Equilibrium state of a Dilute Gas
73
20
Boltzmann's H Theorem
73
2
The Maxwell-Boltzmann Distribution
75
4
The Method of the Most Probable Distribution
79
6
Analysis of the H Theorem
85
5
The Poincare Cycle
90
3
Transport Phenomena
93
32
The Mean Free Path
93
2
Effusion
95
1
The Conservation Laws
96
4
The Zero-Order Approximation
100
4
The First-Order Approximation
104
4
Viscosity
108
3
Viscous Hydrodynamics
111
2
The Navier-Stokes Equation
113
4
Example in Hydrodynamics
117
8
PART B STATISTICAL MECHANICS
125
180
Classical Statistical Mechanics
127
16
The Postulate of Classical Statistical Mechanics
127
3
Microcanonical Ensemble
130
5
Derivationi of Thermodynamics
135
1
Equipartition Theorem
136
2
Classical Ideal Gas
138
2
Gibbs Paradox
140
3
Canonical Ensemble and Grand Canonical Ensemble
143
28
Canonical Ensemble
143
2
Energy Fluctuations in the Canonical Ensemble
145
4
Grand Canonical Ensemble
149
3
Density Fluctuations in the Grand Canonical Ensemble
152
2
The Chemical Potential
154
3
Equivalence of the Canonical Ensemble and the Grand Canonical Ensemble
157
4
Behavior of W(N)
161
2
The Meaning of the Maxwell Construction
163
8
Quantum statistical mechanics
171
22
The Postulates of Quantum Statistical Mechanics
171
3
Density Matrix
174
2
Ensembles in Quantum Statistical Mechanics
176
2
The Third Law of Thermodynamics
178
1
The Ideal Gases: Microcanonical Ensemble
179
6
The Ideal Gases: Grand Canonical Ensemble
185
4
Foundations of Statistical Mechanics
189
4
General Properties of the Partition Function
193
20
The Darwin-Fowler Method
193
6
Classical Limit of the Partition Function
199
7
Singularities and Phase Transitions
206
4
The Lee-Yang Circle Theorem
210
3
Approximate Methods
213
28
Classical Cluster Expansion
213
7
Quantum Cluster Expansion
220
4
The Second Virial Coefficient
224
4
Variational Principles
228
2
Imperfect Gases at Low Temperatures
230
11
Fermi Systems
241
37
The Equation of State of an Ideal Fermi Gas
241
6
The Theory of White Dwarf Stars
247
6
Landau Diamagnetism
253
7
The De Haas-Van Alphen Effect
260
1
The Quantized Hall Effect
261
6
Pauli Paramagnetism
267
5
Magnetic Properties of an Imperfect Gas
272
6
Bose Systems
278
27
Photons
278
5
Phonons in Solids
283
3
Bose-Einnstein Condensation
286
8
An Imperfect Bose Gas
294
4
The Superfluid Order Parameter
298
7
PART C SPECIAL TOPICS IN STATISTICAL MECHANICS
305
163
Superfluids
307
34
Liquid Helium
307
4
Tisza's Two-Fluid Model
311
2
The Bose-Einstein Condensate
313
2
Landau's Theory
315
2
Superfluid Velocity
317
4
Superfluid Flow
321
4
The Phonon Wave Function
325
4
Dilute Bose Gas
329
12
The Ising Model
341
27
Definition of the Ising Model
341
3
Equivalence of the Ising Model to Other Models
344
4
Spontaneous Magnetization
348
4
The Bragg-Williams Approximation
352
5
The Bethe-Peierls Approximation
357
4
The One-Dimensional Ising Model
361
7
The Onsager Solution
368
24
Formulation of the Two-Dimensional Ising Model
368
6
Mathematical Digression
374
4
The Solution
378
14
Critical Phenomena
392
24
The Order Parameter
392
2
The Correlation Function and the Fluctuation-Dissipation Theorem
394
2
Critical Exponents
396
3
The Scaling Hypothesis
399
4
Scale Invariance
403
3
Goldstone Excitations
406
1
The Importance of Dimensionality
407
9
The Landau Approach
416
25
The Landau Free Energy
416
2
Mathematical Digression
418
2
Derivation in Simple Models
420
2
Mean-Field Theory
422
4
The Van der Waals Equation of State
426
2
The Tricritical Point
428
6
The Gaussian Model
434
3
The Ginzburg Criterion
437
1
Anomalous Dimensions
438
3
Renoremalization Group
441
27
Block Spins
441
2
The One-Dimensional Ising Model
443
3
Renormalization-Group Transformation
446
3
Fixed Points and Scaling Fields
449
3
Momentum-Space Formulation
452
3
The Gaussian Model
455
3
The Landau-Wilson Model
458
10
APPENDIX N-BODY SYSTEM OF IDENTICAL PARTICLES
468
19
A.1 The Two Kinds of Statistics
468
2
A.2 N-Body Wave Functions
470
7
A.3 Method of Quantized Fields
477
7
A.4 Longitudinal Sum Rules
484
3
Index
487