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Preface
6
Contents
9
1 Basic Concepts of Thermodynamicsand Statistical Physics
13
1.1 Macroscopic Description of State of Systems: Postulates of Thermodynamics
13
1.2 Mechanical Description of Systems: Microscopic State:Phase Space: Quantum States
18
1.3 Statistical Description of Classical Systems: Distribution Function: Liouville Theorem
25
1.4 Microcanonical Distribution: Basic Postulate of Statistical Physics
31
1.5 Statistical Description of Quantum Systems: Statistical Matrix: Liouville Equation
34
1.6 Entropy and Statistical Weight
39
1.7 Law of Increasing Entropy:Reversible and Irreversible Processes
43
1.8 Absolute Temperature and Pressure: Basic Thermodynamic Relationship
47
2 Law of Thermodynamics: Thermodynamic Functions
54
2.1 First Law of Thermodynamics:Work and Amount of Heat: Heat Capacity
54
2.2 Second Law of Thermodynamics: Carnot Cycle
61
2.3 Thermodynamic Functions of Closed Systems: Method of Thermodynamic Potentials
67
2.4 Thermodynamic Coefficients and General Relationships Between Them
74
2.5 Thermodynamic Inequalities: Stability of Equilibrium State of Homogeneous Systems
80
2.6 Third Law of Thermodynamics: Nernst Principle
85
2.7 Thermodynamic Relationships for Dielectrics and Magnetics
90
2.8 Magnetocaloric Effect:Production of Ultra-Low Temperatures
94
2.9 Thermodynamics of Systems with Variable Number of Particles: Chemical Potential
97
2.10 Conditions of Equilibrium of Open Systems
101
3 Canonical Distribution: Gibbs Method
104
3.1 Gibbs Canonical Distribution for Closed Systems
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3.2 Free Energy: Statistical Sum and Statistical Integral
110
3.3 Gibbs Method and Basic Objects of its Application
113
3.4 Grand Canonical Distribution for Open Systems
114
4 Ideal Gas
120
4.1 Free Energy, Entropy and Equationof the State of an Ideal Gas
120
4.2 Mixture of Ideal Gases: Gibbs Paradox
123
4.3 Law About Equal Distribution of Energy Over Degrees of Freedom: Classical Theory of Heat Capacityof an Ideal Gas
126
4.3.1 Classical Theory of Heat Capacity of an Ideal Gas
129
4.4 Quantum Theory of Heat Capacity of an Ideal Gas: Quantization of Rotational and Vibrational Motions
131
4.4.1 Translational Motion
133
4.4.2 Rotational Motion
136
4.4.3 Vibrational Motion
139
4.4.4 Total Heat Capacity
142
4.5 Ideal Gas Consisting of Polar Molecules in an External Electric Field
144
4.5.1 Orientational Polarization
144
4.5.2 Entropy: Electrocaloric Effect
148
4.5.3 Mean Value of Energy: Caloric Equation of State
149
4.5.4 Heat Capacity: Determination of Electric Dipole Moment of Molecule
150
4.6 Paramagnetic Ideal Gas in External Magnetic Field
152
4.6.1 Classical Case
152
4.6.2 Quantum Case
154
Magnetization
156
Entropy, Mean Energy and Heat Capacity
158
4.7 Systems with Negative Absolute Temperature
161
5 Non-Ideals Gases
167
5.1 Equation of State of Rarefied Real Gases
167
5.2 Second Virial Coefficient and Thermodynamics of Van Der Waals Gas
174
5.3 Neutral Gas Consisting of Charged Particles: Plasma
179
6 Solids
185
6.1 Vibration and Waves in a Simple Crystalline Lattice
185
6.1.1 One-Dimensional Simple Lattice
188
6.1.2 Three-Dimensional Simple Crystalline Lattice
192
6.2 Hamilton Function of Vibrating Crystalline Lattice: Normal Coordinates
194
6.3 Classical Theory of Thermodynamic Properties of Solids
197
6.4 Quantum Theory of Heat Capacity of Solids: Einstein and Debye Models
204
6.4.1 Einstein's Theory
206
6.4.2 Debye's Theory
207
6.5 Quantum Theory of Thermodynamic Properties of Solids
214
7 Quantum Statistics: Equilibrium Electron Gas
223
7.1 Boltzmann Distribution: Difficulties of Classical Statistics
224
7.2 Principle of Indistinguishability of Particles: Fermions and Bosons
232
7.3 Distribution Functions of Quantum Statistics
239
7.4 Equations of States of Fermi and Bose Gases
244
7.5 Thermodynamic Properties of Weakly Degenerate Fermi and Bose Gases
247
7.6 Completely Degenerate Fermi Gas: Electron Gas: Temperature of Degeneracy
250
7.7 Thermodynamic Properties of Strongly Degenerate Fermi Gas: Electron Gas
254
7.8 General Case: Criteria of Classicity and Degeneracy of Fermi Gas: Electron Gas
259
7.8.1 Low Temperatures
260
7.8.2 High Temperatures
261
7.8.3 Moderate Temperatures: TT0
261
7.9 Heat Capacity of Metals:First Difficulty of Classical Statistics
264
7.9.1 Low Temperatures
266
7.9.2 Region of Temperatures
266
7.10 Pauli Paramagnetism: Second Difficulty of Classical Statistics
268
7.11 ``Ultra-Relativistic'' Electron Gas in Semiconductors
272
7.12 Statistics of Charge Carriers in Semiconductors
275
7.13 Degenerate Bose Gas: Bose–Einstein Condensation
287
7.14 Photon Gas: Third Difficulty of Classical Statistics
292
7.15 Phonon Gas
299
8 Electron Gas in Quantizing Magnetic Field
307
8.1 Motion of Electron in External Uniform Magnetic Field: Quantization of Energy Spectrum
307
8.2 Density of Quantum States in Strong Magnetic Field
312
8.3 Grand Thermodynamic Potential and Statistics of Electron Gas in Quantizing Magnetic Field
314
8.4 Thermodynamic Properties of Electron Gas in Quantizing Magnetic Field
320
8.5 Landau Diamagnetism
324
9 Non-Equilibrium Electron Gas in Solids
330
9.1 Boltzmann Equation and Its Applicability Conditions
330
9.1.1 Nonequilibrium Distribution Function
330
9.1.2 Boltzmann Equation
332
9.1.3 Applicability Conditions of the Boltzmann Equation
334
9.2 Solution of Boltzmann Equation in Relaxation Time Approximation
337
9.2.1 Relaxation Time
337
9.2.2 Solution of the Boltzmann Equation in the Absence of Magnetic Field
339
9.2.3 Solution of Boltzmann Equation with an Arbitrary Nonquantizing Magnetic Field
345
9.3 General Expressions of Main Kinetic Coefficients
349
9.3.1 Current Density and General Formof Conductivity Tensors
349
9.3.2 General Expressions of Main Kinetic Coefficients
351
Galvanomagnetic Effects
351
Thermomagnetic Effects
351
9.4 Main Relaxation Mechanisms
353
9.4.1 Charge Carrier Scattering by Ionized Impurity Atoms
354
9.4.2 Charge Carrier Scattering by Phonons in Conductorswith Arbitrary Isotropic Band
357
Scattering by Acoustic Phonons, Deformation Potential Method
357
Scattering by Nonpolar Optical Phonons, Deformation Potential Method
360
Scattering by Polar Optical Phonons
363
9.4.3 Generalized Formula for Relaxation Time
366
9.5 Boltzmann Equation Solution for Anisotropic Band in Relaxation Time Tensor Approximation
368
9.5.1 Current Density
368
9.5.2 The Boltzmann Equation Solution
369
9.5.3 Current Density
371
Definite Integrals Frequently Met in Statistical Physics
372
A.1 Gamma-Function or Euler Integral of Second Kind
372
A.2 Integral of Type
373
A.3 Integral of Type
374
A.4 Integral of Type
375
A.5 Integral of Type
376
Jacobian and Its Properties
378
Bibliograpy
379
Index
381
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