A modern course in statistical physics:
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| Format: | Book |
| Language: | English |
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Wiley-VCH
2004
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| Edition: | 2. ed., [Nachdr.] |
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| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIX, 822 S. Ill., graph. Darst. |
| ISBN: | 0471595209 9780471595205 |
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| 100 | 1 | |a Reichl, Linda E. |d 1942- |e Verfasser |0 (DE-588)138557241 |4 aut | |
| 245 | 1 | 0 | |a A modern course in statistical physics |c L. E. Reichl |
| 250 | |a 2. ed., [Nachdr.] | ||
| 264 | 1 | |a Weinheim |b Wiley-VCH |c 2004 | |
| 300 | |a XIX, 822 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 0 | 7 | |a Thermodynamik |0 (DE-588)4059827-5 |2 gnd |9 rswk-swf |
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| _version_ | 1804135028734558208 |
|---|---|
| adam_text | CONTENTS
Preface
xix
1.
Introduction
1
I.A.
Overview
1
1.В.
Plan of Book
2
l.C. Use as a Textbook
5
PART ONE THERMODYNAMICS
2.
Introduction to Thermodynamics
9
2.A. Introductory Remarks
9
11
16
16
17
18
19
19
20
20
21
21
22
22
23
31
33
36
37
40
42
45
48
vii
2.B.
State Variables and Exact Differentials
2.C.
Some Mechanical Equations of State
2.С.1.
Ideal Gas Law
2.C.2.
Virial Expansion
2.C.3.
Van
der Waals
Equation of State
2.C.4.
Solids
2.C.5.
Elastic Wire or Rod
2.C.6.
Surface Tension
2.C.7.
Electric Polarization
2.C.8.
Curie s Law
2.D.
The Laws of Thermodynamics
2.D.I.
Zeroth Law
2.D.2.
First Law
2.D.3.
Second Law
2.D.4.
Third Law
2.E.
Fundamental Equation of Thermodynamics
2.F.
Thermodynamic Potentials
2.F.I.
Internal Energy
2.F.2.
Enthalpy
2.F.3.
Helmholz
Free Energy
2.F.4.
Gibbs Free Energy
2.F.5.
Grand Potential
iii
CONTENTS
2.G.
Response Functions
50
2.G.I. Thermal Response Functions (Heat Capacity)
50
2.G.2. Mechanical Response Functions
53
2.H.
Stability of the Equilibrium State
55
2.Н.1.
Conditions for Local Equilibrium
in a PVT System
55
2.H.2. Conditions for Local Stability in a PVT System
57
2.H.3. Implications of the Stability Requirements for
the Free Energies
63
S2.A.
Cooling and Liquefactions of Gases
66
S2.A.1. The Joule Effect: Free Expansion
66
S2.A.2. The Joule-Kelvin Effect: Throttling
68
S2.B.
Entropy of Mixing and the Gibbs Paradox
72
S2.C.
Osmotic Pressure in Dilute Solutions
74
S2.D.
The Thermodynamics of Chemical Reactions
78
S2.D.1. The Affinity
78
S2.D.2. Stability
82
S2.E.
The Thermodynamics of Electrolytes
86
References
89
Problems
90
3.
The Thermodynamics of Phase Transitions
96
ЗА.
Introductory Remarks
96
3.B.
Coexistence of Phases: Gibbs Phase Rule
98
3.C.
Classification of Phase Transitions
100
3.D.
Pure PVT Systems
103
3.ΌΛ.
Phase Diagrams
103
3.D.2. Coexistence Curves: Clausius-Clapyron
Equation
105
3.D.3. Liquid-Vapor Coexistence Region
110
3.D.4. The van
der Waals
Equation
115
3.E.
Superconductors
118
3.F.
The Helium Liquids
123
3.F.I. Liquid He4
123
3.F.2. Liquid He3
124
3.F.3. Liquid He3-He4 Mixtures
126
3.G.
Landau Theory
128
3
.G.
1.
Continuous Phase Transitions
128
3.G.2. First-Order Transitions
134
CONTENTS ix
З.Н.
Critical Exponents
135
З.Н.1.
Definition of Critical Exponents
136
3.H.2. The Critical Exponents for Pure PVT Systems
137
S3.A. Surface Tension
142
S3.B. Thermomechanical Effect
146
S3.C. The Critical Exponents for the Curie Point
149
S3.D. Tricritical Points
151
S3.E. Binary Mixtures
153
S3.E.1. Stability Conditions
154
S3.E.2. Equilibrium Conditions
155
S3.E.3. Coexistence Curve
160
S3.F. The Ginzburg-Landau Theory of Superconductors
162
References
166
Problems
167
PART TWO CONCEPTS FROM PROBABILITY THEORY
4.
Elementary Probability Theory and Limit Theorems
173
4.A. Introduction
173
4.B. Permutations and Combinations
174
4.C. Definition of Probability
175
4.D. Stochastic Variables and Probability
177
4.D.I. Distribution Functions
178
4.D.2. Moments
180
4.D.3. Characteristic Functions
182
4.D.4. Jointly Distributed Stochastic Variables
183
4.E. Binomial Distributions
188
4.Е.1.
The Binomial Distribution
188
4.E.2. The Gaussian (For Normal) Distribution
191
4.E.3. The
Poisson
Distribution
192
4.E.4. Binomial Random Walk
194
4.F. A Central Limit Theorem and Law of Large Numbers
197
4.F.I. A Central Limit Theorem
197
4.F.2. The Law of Large Numbers
198
S4.A. Lattice Random Walk
199
S4.A.1. One-Dimensional Lattice
200
S4.A.2. Random Walk in Higher Dimension
203
x
CONTENTS
S4.B.
Infinitely Divisible Distributions
207
S4.B.1. Gaussian Distribution
208
S4.B.2.
Poisson
Distribution
209
S4.B.3. Cauchy Distribution
209
S4.B.4. Levy Distribution
210
S4.C. The Central Limit Theorem
211
S4.C.
1.
Useful Inequalities
212
S4.C.2. Convergence to a Gaussian
213
S4.D.
Weierstrass
Random Walk
214
S4.D.1. Discrete One-Dimensional Random Walk
215
S4.D.2. Continuum Limit of One-Dimensional Discrete
Random Walk
217
S4.D.3. Two-Dimensional Discrete Random Walk
(Levy Flight)
218
S4.E. General Form of Infinitely Divisible Distributions
221
S4.E.1. Levy-Khintchine Formula
222
S4.E.2. Kolmogorov Formula
223
References
225
Problems
225
5.
Stochastic Dynamics and Brownian Motion
229
5.A. Introduction
229
5.B. General Theory
231
5.C. Markov Chains
234
5.С.1.
Spectral Properties
234
5.C.2. Random Walk
240
5.D. The Master Equation
241
5.D.I.
Derivation of the Master Equation
242
5.D.2. Detailed Balance
244
5.D.3. Mean First Passage Time
247
5.E. Brownian Motion
250
5.Е.1.
Langevin
Equation
251
5.E.2. The Spectral Density (Power Spectrum)
254
S5.A. Time Periodic Markov Chain
258
S5.B. Master Equation for Birth-Death Processes
260
SS-B.l. The Master Equation
260
853.2.
Linear Birth-Death Processes
261
S5.B.3. Nonlinear Birth-Death Processes
265
CONTENTS xi
Ѕб.С.
The Fokker-Planck Equation
266
SS.C.l. Probability Flow in Phase Space
266
85.0.2.
Probability Flow for Brownian Particle
267
S5.C3. The Strong Friction Limit
270
S5.C.4. Solution of Fokker-Planck Equations with
One Variable
271
S5.D. Approximations to the Master Equation
276
References
278
Problems
279
6.
The Foundations of Statistical Mechanics
285
6.A. Introduction
285
6.B. The Liouville Equation of Motion
286
6.C. Ergodic Theory and the Foundation of Statistical Mechanics
296
6.D. The Quantum Probability Density Operator
303
S6.A. Reduced Probability Densities and the BBGKY ffierarchy
310
S6.B. Reduced Density Matrices and the Wigner Distribution
314
S6.C. Microscopic Balance Equations
319
S6.D. Mixing Flow
321
S6.E. Anharmonic Oscillator Systems
326
S6.F. Newtonian Dynamics and Irreversibility
334
References
335
Problems
336
PART THREE EQUILIBRIUM STATISTICAL MECHANICS
7.
Equilibrium Statistical Mechanics
341
7.A. Introduction
341
7.B. The Microcanonical Ensemble
343
7.C. Einstein Fluctuation Theory
349
7.С.1.
General Discussion
349
7.C.2. Fluid Systems
351
7.D. The Canonical Ensemble
354
7.D.I. Probability Density Operator
354
7.D.2. Systems of Indistinguishable Particles
357
7.D.3. Systems of Distinguishable Particles
362
7.E. Heat Capacity of a Debye Solid
364
xii CONTENTS
7.F.
Order-Disorder Transitions
369
7.F.I. Exact Solution for a One-Dimensional Lattice
370
7.F.2. Mean Field Theory for a d-Dimensional Lattice
372
7.G. The Grand Canonical Ensemble
377
7.H. Ideal Quantum Gases
381
7.Н.1.
Bose-Einstein Gases
383
7.H.2. Fermi-Dirac Ideal Gases
392
S7.A. Heat Capacity of Lattice Vibrations on a One-
Dimensional Lattice
—
Exact Solution
401
S7.A.1. Exact Expression
—
Large
N 404
S7.A.2. Continuum Approximation
—
Large
N 406
S7.B. Momentum Condensation in an Interacting Fermi Fluid
407
S7.C. The Yang-Lee Theory of Phase Transitions
418
References
422
Problems
423
8.
Order-Disorder Transitions and
Renormalizatíon
Theory
427
8-А.
Introduction
427
8.B. Static Correlation Functions and Response Functions
428
8.В.1.
General Relations
429
8.B.2. Application to the Ising Lattice
431
8.C. Scaling
433
8.С.1.
Homogeneous Functions
433
8.C.2.
Widom
Scaling
434
8.C.3. Kadanoff Scaling
437
8.D. Microscopic Calculation of Critical Exponents
440
S8.A. Critical Exponents for the S4 Model
448
S8.B. Exact Solution of the Two-Dimensional Ising Model
462
S8.B.1. Partition Function
462
S8.B.2. Antisymmetric Matrices and Dimer Graphs
466
S8.B.3. Closed Graphs and Mixed Dimer Graphs
469
S8.B.4. Partition Function for Infinite Planar Lattice
475
References
485
Problems
486
9.
Interacting Fluids
488
9.A. Introduction
488
9.B. Thermodynamics and the Radial Distribution Function
489
CONTENTS xiii
9.C.
Vinal
Expansion
of the Equation of State
492
9.С.1.
Vinal
Expansions and Cluster Functions
493
9.C.2. The Second Virial Coefficient
500
9.C.3. Higher-Order Virial Coefficients
506
S9.A. The Pressure and Compressibility Equations
507
S9.A.1. The Pressure Equation
508
S9.A.2. The Compressibility Equation
509
S9.B. Ornstein-Zernicke Equation
510
S9.C. Third Virial Coefficient
513
S9.C.1. Square-Well Potential
514
S9.C.2. Lennard-Jones
6-12
Potential
515
S9.D. Virial Coefficients for Quantum Gases
517
References
526
Problems
527
PART FOUR NONEQUILIBRIUM STATISTICAL MECHANICS
10.
Hydrodynamic Processes Near Equilibrium
531
10.A. Introduction
531
10.B. Navier-Stokes Hydrodynamic Equations
533
10.B.1. Balance Equations
534
10.B.2. Entropy Source and Entropy Current
537
10.B.3. Transport Coefficients
541
10.C. Linearized Hydrodynamic Equations
544
lO.C.l. Linearization of the Hydrodynamic Equations
545
10.C.2. Transverse Hydrodynamic Modes
549
10.C.3. Longitudinal Hydrodynamic Modes
550
10.D. Dynamic Equilibrium Fluctuations and Transport Processes
552
10.D.1. Onsager s Relations
553
10.D.2. Weiner-Khintchine Theorem
557
10.E. Linear Response Theory and the Fluctuation-Dissipation
Theorem
561
10.E.1. The Response Matrix
562
10.E.2. Causality
563
10.E.3. The Fluctuation-Dissipation Theorem
568
10.E.4. Power Absorption
570
10.F. Transport Properties of Mixtures
574
lO.F.l. Entropy Production in Multicomponent Systems
574
xiv CONTENTS
ÏO.F.L Fick s
Law for
Diffusion 580
10.F.3.
Thermal
Diffusion 582
10.F.4.
Electrical Conductivity and Diffusion in Fluids
583
S
10.
A. Onsager s Relations When a Magnetic Field is Present
586
S10.B. Microscopic Linear Response Theory
589
S10.C. Light Scattering
592
SlO.C.l. Scattered Electric Field
594
SIO.C^. Intensity of Scattered Light
597
S10.D. Thermoelectricity
600
S10.D.1. The Peltier Effect
601
S10.D.2. The Seebeck Effect
603
S10.D.3. Thomson Heat
605
SI
O.E.
Entropy Production in Discontinuous Systems
605
SI O.E.I. Volume Flow Across a Membrane
606
S10.E.2. Ion Transport Across a Membrane
610
S10.F. Stochastic Hydrodynamics
612
S10.F.1. Stochastic Hydrodynamic Equations
613
S10.F.2. Properties of Equilibrium Correlation Functions
614
S10.F.3. Random Current Correlation Functions
617
S10.G.
Long-Time
Tails
620
S10.G.1. Fluid Flow Around the Brownian Particle
621
S10.G.2. Drag Force on the Brownian Particle
623
S10.G.3. Velocity Autocorrelation Function
624
S10.H. Superfluid Hydrodynamics
631
SI O.H.I. Superfluid Hydrodynamic Equations
631
S10.H.2. Sound Modes
635
SI
0.1.
General Definition of Hydrodynamic Modes
639
510.1.1. Projection Operators
640
510.1.2. Conserved Quantities
642
S 10.I.3.
Hydrodynamic Modes Due to Broken Symmetry
644
References
649
Problems
650
11.
Transport Theory
656
H.A.
Introduction
656
ll.B. Elementary Transport Theory
657
11
.B.I
.
The Maxwell-Boltzmann Distribution
657
11.B.2. The Mean Free Path
658
CONTENTS xv
П.В.З.
The
Collision
Frequency
659
11.
В
.4.
Self-Diffusion
661
П-В-б.
The Coefficients of Viscosity and
Thermal Conductivity
664
11.B.6. The Rate of Reaction
666
U.C.
The Boltzmann Equation
670
11
.C.
1.
Two-Body Scattering
671
H.C.2. Derivation of the Boltzmann Equation
679
11.C.3. Boltzmann s
H
Theorem
680
ll.D. Linearized Boltzmann and Lorentz-Boltzmann Equations
682
11.D.I.
Kinetic Equations for a Two-Component Gas
682
11.D.2. Collision Operators
684
U.E.
Coefficient of Self-Diffusion
688
11.
E.I. Derivation of the Diffusion Equation
688
11.E.2. Eigenfrequencies of the Lorentz-
Boltzmann Equation
690
11.F. Coefficients of Viscosity and Thermal Conductivity
691
11.
F.I. Derivation of the Hydrodynamic Equations
692
1
l.F.2. Eigenfrequencies of the Boltzmann Equation
697
11.F.3. Shear Viscosity and Thermal Conductivity
700
ll.G. Computation of Transport Coefficients
701
11.
G.I.
Sonine
Polynomials
702
11.0.2.
Diffusion Coefficient
703
11.G.3. Thermal Conductivity
704
11.G.4. Shear Viscosity
708
S
11.
A. Beyond the Boltzmann Equation
710
References
717
Problems
718
12.
Nonequilibrium Phase Transitions
721
12.
A. Introduction
721
12.B. Nonequilibrium Stability Criteria
722
12.B.1. Stability Conditions Near Equilibrium
723
12.B.2. Stability Conditions Far From Equilibrium
726
12.C. The Schlogl Model
732
12.D. The Brasselator
735
12.D.1. The Brusselator
—
A Nonlinear
Chemical Model
736
12.D.2. Boundary Conditions
737
xvi CONTENTS
12.D.3. Linear
Stability Analysis
739
12.E. The
Rayleigh-Bénard
Instability
742
И.ЕЛ.
Hydrodynamic Equations and
Boundary Conditions
743
12.E.2. Linear Stability Analysis
747
S
12.
A. Fluctuations Near a Nonequilibrium Phase Transition
753
S12.A.1. Fluctuations in the
Rayleigh-Bénard
System
753
S12.A.2. Fluctuations in the Brusselator
760
S12.A.3. The Time-Dependent Ginzburg-Landau Equation
764
References
765
Problems
767
APPENDICES
A. Balance Equations
768
A.I. General Fluid Flow
768
A.2. General Balance Equation
771
References
773
B. Systems of Identical Particles
774
B.I. Position and Momentum Eigenstates
774
B.I.I. Free Particle
775
B.I.
2.
Particle in a Box
776
B.2. Symmetrized iV-Particle Position and
Momentum Eigenstates
777
B.2.1. Symmetrized Momentum Eigenstates for
Bose-Einstein Particles
778
B.2.2. Antisymmetrized Momentum Eigenstates
for Fermi-Dirac Particles
779
B.2.3. Partition Functions and Expectation Values
780
B.3. The Number Representation
781
B.3.1. The Number Representation for Bosons
782
B.3.2. The Number Representation for
Fermions
785
B.3.3. Field Operators
788
References
790
C. Stability of Solutions to Nonlinear Equations
791
C.I. Linear Stability Theory
791
CONTENTS xvii
C.2. Limit
Cycles
795
С.З.
Liapounov
Functions and Global Stability
796
References
798
Author Index
799
Subject Index
804
|
| adam_txt |
CONTENTS
Preface
xix
1.
Introduction
1
I.A.
Overview
1
1.В.
Plan of Book
2
l.C. Use as a Textbook
5
PART ONE THERMODYNAMICS
2.
Introduction to Thermodynamics
9
2.A. Introductory Remarks
9
11
16
16
17
18
19
19
20
20
21
21
22
22
23
31
33
36
37
40
42
45
48
vii
2.B.
State Variables and Exact Differentials
2.C.
Some Mechanical Equations of State
2.С.1.
Ideal Gas Law
2.C.2.
Virial Expansion
2.C.3.
Van
der Waals
Equation of State
2.C.4.
Solids
2.C.5.
Elastic Wire or Rod
2.C.6.
Surface Tension
2.C.7.
Electric Polarization
2.C.8.
Curie's Law
2.D.
The Laws of Thermodynamics
2.D.I.
Zeroth Law
2.D.2.
First Law
2.D.3.
Second Law
2.D.4.
Third Law
2.E.
Fundamental Equation of Thermodynamics
2.F.
Thermodynamic Potentials
2.F.I.
Internal Energy
2.F.2.
Enthalpy
2.F.3.
Helmholz
Free Energy
2.F.4.
Gibbs Free Energy
2.F.5.
Grand Potential
iii
CONTENTS
2.G.
Response Functions
50
2.G.I. Thermal Response Functions (Heat Capacity)
50
2.G.2. Mechanical Response Functions
53
2.H.
Stability of the Equilibrium State
55
2.Н.1.
Conditions for Local Equilibrium
in a PVT System
55
2.H.2. Conditions for Local Stability in a PVT System
57
2.H.3. Implications of the Stability Requirements for
the Free Energies
63
S2.A.
Cooling and Liquefactions of Gases
66
S2.A.1. The Joule Effect: Free Expansion
66
S2.A.2. The Joule-Kelvin Effect: Throttling
68
S2.B.
Entropy of Mixing and the Gibbs Paradox
72
S2.C.
Osmotic Pressure in Dilute Solutions
74
S2.D.
The Thermodynamics of Chemical Reactions
78
S2.D.1. The Affinity
78
S2.D.2. Stability
82
S2.E.
The Thermodynamics of Electrolytes
86
References
89
Problems
90
3.
The Thermodynamics of Phase Transitions
96
ЗА.
Introductory Remarks
96
3.B.
Coexistence of Phases: Gibbs Phase Rule
98
3.C.
Classification of Phase Transitions
100
3.D.
Pure PVT Systems
103
3.ΌΛ.
Phase Diagrams
103
3.D.2. Coexistence Curves: Clausius-Clapyron
Equation
105
3.D.3. Liquid-Vapor Coexistence Region
110
3.D.4. The van
der Waals
Equation
115
3.E.
Superconductors
118
3.F.
The Helium Liquids
123
3.F.I. Liquid He4
123
3.F.2. Liquid He3
124
3.F.3. Liquid He3-He4 Mixtures
126
3.G.
Landau Theory
128
3
.G.
1.
Continuous Phase Transitions
128
3.G.2. First-Order Transitions
134
CONTENTS ix
З.Н.
Critical Exponents
135
З.Н.1.
Definition of Critical Exponents
136
3.H.2. The Critical Exponents for Pure PVT Systems
137
S3.A. Surface Tension
142
S3.B. Thermomechanical Effect
146
S3.C. The Critical Exponents for the Curie Point
149
S3.D. Tricritical Points
151
S3.E. Binary Mixtures
153
S3.E.1. Stability Conditions
154
S3.E.2. Equilibrium Conditions
155
S3.E.3. Coexistence Curve
160
S3.F. The Ginzburg-Landau Theory of Superconductors
162
References
166
Problems
167
PART TWO CONCEPTS FROM PROBABILITY THEORY
4.
Elementary Probability Theory and Limit Theorems
173
4.A. Introduction
173
4.B. Permutations and Combinations
174
4.C. Definition of Probability
175
4.D. Stochastic Variables and Probability
177
4.D.I. Distribution Functions
178
4.D.2. Moments
180
4.D.3. Characteristic Functions
182
4.D.4. Jointly Distributed Stochastic Variables
183
4.E. Binomial Distributions
188
4.Е.1.
The Binomial Distribution
188
4.E.2. The Gaussian (For Normal) Distribution
191
4.E.3. The
Poisson
Distribution
192
4.E.4. Binomial Random Walk
194
4.F. A Central Limit Theorem and Law of Large Numbers
197
4.F.I. A Central Limit Theorem
197
4.F.2. The Law of Large Numbers
198
S4.A. Lattice Random Walk
199
S4.A.1. One-Dimensional Lattice
200
S4.A.2. Random Walk in Higher Dimension
203
x
CONTENTS
S4.B.
Infinitely Divisible Distributions
207
S4.B.1. Gaussian Distribution
208
S4.B.2.
Poisson
Distribution
209
S4.B.3. Cauchy Distribution
209
S4.B.4. Levy Distribution
210
S4.C. The Central Limit Theorem
211
S4.C.
1.
Useful Inequalities
212
S4.C.2. Convergence to a Gaussian
213
S4.D.
Weierstrass
Random Walk
214
S4.D.1. Discrete One-Dimensional Random Walk
215
S4.D.2. Continuum Limit of One-Dimensional Discrete
Random Walk
217
S4.D.3. Two-Dimensional Discrete Random Walk
(Levy Flight)
218
S4.E. General Form of Infinitely Divisible Distributions
221
S4.E.1. Levy-Khintchine Formula
222
S4.E.2. Kolmogorov Formula
223
References
225
Problems
225
5.
Stochastic Dynamics and Brownian Motion
229
5.A. Introduction
229
5.B. General Theory
231
5.C. Markov Chains
234
5.С.1.
Spectral Properties
234
5.C.2. Random Walk
240
5.D. The Master Equation
241
5.D.I.
Derivation of the Master Equation
242
5.D.2. Detailed Balance
244
5.D.3. Mean First Passage Time
247
5.E. Brownian Motion
250
5.Е.1.
Langevin
Equation
251
5.E.2. The Spectral Density (Power Spectrum)
254
S5.A. Time Periodic Markov Chain
258
S5.B. Master Equation for Birth-Death Processes
260
SS-B.l. The Master Equation
260
853.2.
Linear Birth-Death Processes
261
S5.B.3. Nonlinear Birth-Death Processes
265
CONTENTS xi
Ѕб.С.
The Fokker-Planck Equation
266
SS.C.l. Probability Flow in Phase Space
266
85.0.2.
Probability Flow for Brownian Particle
267
S5.C3. The Strong Friction Limit
270
S5.C.4. Solution of Fokker-Planck Equations with
One Variable
271
S5.D. Approximations to the Master Equation
276
References
278
Problems
279
6.
The Foundations of Statistical Mechanics
285
6.A. Introduction
285
6.B. The Liouville Equation of Motion
286
6.C. Ergodic Theory and the Foundation of Statistical Mechanics
296
6.D. The Quantum Probability Density Operator
303
S6.A. Reduced Probability Densities and the BBGKY ffierarchy
310
S6.B. Reduced Density Matrices and the Wigner Distribution
314
S6.C. Microscopic Balance Equations
319
S6.D. Mixing Flow
321
S6.E. Anharmonic Oscillator Systems
326
S6.F. Newtonian Dynamics and Irreversibility
334
References
335
Problems
336
PART THREE EQUILIBRIUM STATISTICAL MECHANICS
7.
Equilibrium Statistical Mechanics
341
7.A. Introduction
341
7.B. The Microcanonical Ensemble
343
7.C. Einstein Fluctuation Theory
349
7.С.1.
General Discussion
349
7.C.2. Fluid Systems
351
7.D. The Canonical Ensemble
354
7.D.I. Probability Density Operator
354
7.D.2. Systems of Indistinguishable Particles
357
7.D.3. Systems of Distinguishable Particles
362
7.E. Heat Capacity of a Debye Solid
364
xii CONTENTS
7.F.
Order-Disorder Transitions
369
7.F.I. Exact Solution for a One-Dimensional Lattice
370
7.F.2. Mean Field Theory for a d-Dimensional Lattice
372
7.G. The Grand Canonical Ensemble
377
7.H. Ideal Quantum Gases
381
7.Н.1.
Bose-Einstein Gases
383
7.H.2. Fermi-Dirac Ideal Gases
392
S7.A. Heat Capacity of Lattice Vibrations on a One-
Dimensional Lattice
—
Exact Solution
401
S7.A.1. Exact Expression
—
Large
N 404
S7.A.2. Continuum Approximation
—
Large
N 406
S7.B. Momentum Condensation in an Interacting Fermi Fluid
407
S7.C. The Yang-Lee Theory of Phase Transitions
418
References
422
Problems
423
8.
Order-Disorder Transitions and
Renormalizatíon
Theory
427
8-А.
Introduction
427
8.B. Static Correlation Functions and Response Functions
428
8.В.1.
General Relations
429
8.B.2. Application to the Ising Lattice
431
8.C. Scaling
433
8.С.1.
Homogeneous Functions
433
8.C.2.
Widom
Scaling
434
8.C.3. Kadanoff Scaling
437
8.D. Microscopic Calculation of Critical Exponents
440
S8.A. Critical Exponents for the S4 Model
448
S8.B. Exact Solution of the Two-Dimensional Ising Model
462
S8.B.1. Partition Function
462
S8.B.2. Antisymmetric Matrices and Dimer Graphs
466
S8.B.3. Closed Graphs and Mixed Dimer Graphs
469
S8.B.4. Partition Function for Infinite Planar Lattice
475
References
485
Problems
486
9.
Interacting Fluids
488
9.A. Introduction
488
9.B. Thermodynamics and the Radial Distribution Function
489
CONTENTS xiii
9.C.
Vinal
Expansion
of the Equation of State
492
9.С.1.
Vinal
Expansions and Cluster Functions
493
9.C.2. The Second Virial Coefficient
500
9.C.3. Higher-Order Virial Coefficients
506
S9.A. The Pressure and Compressibility Equations
507
S9.A.1. The Pressure Equation
508
S9.A.2. The Compressibility Equation
509
S9.B. Ornstein-Zernicke Equation
510
S9.C. Third Virial Coefficient
513
S9.C.1. Square-Well Potential
514
S9.C.2. Lennard-Jones
6-12
Potential
515
S9.D. Virial Coefficients for Quantum Gases
517
References
526
Problems
527
PART FOUR NONEQUILIBRIUM STATISTICAL MECHANICS
10.
Hydrodynamic Processes Near Equilibrium
531
10.A. Introduction
531
10.B. Navier-Stokes Hydrodynamic Equations
533
10.B.1. Balance Equations
534
10.B.2. Entropy Source and Entropy Current
537
10.B.3. Transport Coefficients
541
10.C. Linearized Hydrodynamic Equations
544
lO.C.l. Linearization of the Hydrodynamic Equations
545
10.C.2. Transverse Hydrodynamic Modes
549
10.C.3. Longitudinal Hydrodynamic Modes
550
10.D. Dynamic Equilibrium Fluctuations and Transport Processes
552
10.D.1. Onsager's Relations
553
10.D.2. Weiner-Khintchine Theorem
557
10.E. Linear Response Theory and the Fluctuation-Dissipation
Theorem
561
10.E.1. The Response Matrix
562
10.E.2. Causality
563
10.E.3. The Fluctuation-Dissipation Theorem
568
10.E.4. Power Absorption
570
10.F. Transport Properties of Mixtures
574
lO.F.l. Entropy Production in Multicomponent Systems
574
xiv CONTENTS
ÏO.F.L Fick's
Law for
Diffusion 580
10.F.3.
Thermal
Diffusion 582
10.F.4.
Electrical Conductivity and Diffusion in Fluids
583
S
10.
A. Onsager's Relations When a Magnetic Field is Present
586
S10.B. Microscopic Linear Response Theory
589
S10.C. Light Scattering
592
SlO.C.l. Scattered Electric Field
594
SIO.C^. Intensity of Scattered Light
597
S10.D. Thermoelectricity
600
S10.D.1. The Peltier Effect
601
S10.D.2. The Seebeck Effect
603
S10.D.3. Thomson Heat
605
SI
O.E.
Entropy Production in Discontinuous Systems
605
SI O.E.I. Volume Flow Across a Membrane
606
S10.E.2. Ion Transport Across a Membrane
610
S10.F. Stochastic Hydrodynamics
612
S10.F.1. Stochastic Hydrodynamic Equations
613
S10.F.2. Properties of Equilibrium Correlation Functions
614
S10.F.3. Random Current Correlation Functions
617
S10.G.
Long-Time
Tails
620
S10.G.1. Fluid Flow Around the Brownian Particle
621
S10.G.2. Drag Force on the Brownian Particle
623
S10.G.3. Velocity Autocorrelation Function
624
S10.H. Superfluid Hydrodynamics
631
SI O.H.I. Superfluid Hydrodynamic Equations
631
S10.H.2. Sound Modes
635
SI
0.1.
General Definition of Hydrodynamic Modes
639
510.1.1. Projection Operators
640
510.1.2. Conserved Quantities
642
S 10.I.3.
Hydrodynamic Modes Due to Broken Symmetry
644
References
649
Problems
650
11.
Transport Theory
656
H.A.
Introduction
656
ll.B. Elementary Transport Theory
657
11
.B.I
.
The Maxwell-Boltzmann Distribution
657
11.B.2. The Mean Free Path
658
CONTENTS xv
П.В.З.
The
Collision
Frequency
659
11.
В
.4.
Self-Diffusion
661
П-В-б.
The Coefficients of Viscosity and
Thermal Conductivity
664
11.B.6. The Rate of Reaction
666
U.C.
The Boltzmann Equation
670
11
.C.
1.
Two-Body Scattering
671
H.C.2. Derivation of the Boltzmann Equation
679
11.C.3. Boltzmann's
H
Theorem
680
ll.D. Linearized Boltzmann and Lorentz-Boltzmann Equations
682
11.D.I.
Kinetic Equations for a Two-Component Gas
682
11.D.2. Collision Operators
684
U.E.
Coefficient of Self-Diffusion
688
11.
E.I. Derivation of the Diffusion Equation
688
11.E.2. Eigenfrequencies of the Lorentz-
Boltzmann Equation
690
11.F. Coefficients of Viscosity and Thermal Conductivity
691
11.
F.I. Derivation of the Hydrodynamic Equations
692
1
l.F.2. Eigenfrequencies of the Boltzmann Equation
697
11.F.3. Shear Viscosity and Thermal Conductivity
700
ll.G. Computation of Transport Coefficients
701
11.
G.I.
Sonine
Polynomials
702
11.0.2.
Diffusion Coefficient
703
11.G.3. Thermal Conductivity
704
11.G.4. Shear Viscosity
708
S
11.
A. Beyond the Boltzmann Equation
710
References
717
Problems
718
12.
Nonequilibrium Phase Transitions
721
12.
A. Introduction
721
12.B. Nonequilibrium Stability Criteria
722
12.B.1. Stability Conditions Near Equilibrium
723
12.B.2. Stability Conditions Far From Equilibrium
726
12.C. The Schlogl Model
732
12.D. The Brasselator
735
12.D.1. The Brusselator
—
A Nonlinear
Chemical Model
736
12.D.2. Boundary Conditions
737
xvi CONTENTS
12.D.3. Linear
Stability Analysis
739
12.E. The
Rayleigh-Bénard
Instability
742
И.ЕЛ.
Hydrodynamic Equations and
Boundary Conditions
743
12.E.2. Linear Stability Analysis
747
S
12.
A. Fluctuations Near a Nonequilibrium Phase Transition
753
S12.A.1. Fluctuations in the
Rayleigh-Bénard
System
753
S12.A.2. Fluctuations in the Brusselator
760
S12.A.3. The Time-Dependent Ginzburg-Landau Equation
764
References
765
Problems
767
APPENDICES
A. Balance Equations
768
A.I. General Fluid Flow
768
A.2. General Balance Equation
771
References
773
B. Systems of Identical Particles
774
B.I. Position and Momentum Eigenstates
774
B.I.I. Free Particle
775
B.I.
2.
Particle in a Box
776
B.2. Symmetrized iV-Particle Position and
Momentum Eigenstates
777
B.2.1. Symmetrized Momentum Eigenstates for
Bose-Einstein Particles
778
B.2.2. Antisymmetrized Momentum Eigenstates
for Fermi-Dirac Particles
779
B.2.3. Partition Functions and Expectation Values
780
B.3. The Number Representation
781
B.3.1. The Number Representation for Bosons
782
B.3.2. The Number Representation for
Fermions
785
B.3.3. Field Operators
788
References
790
C. Stability of Solutions to Nonlinear Equations
791
C.I. Linear Stability Theory
791
CONTENTS xvii
C.2. Limit
Cycles
795
С.З.
Liapounov
Functions and Global Stability
796
References
798
Author Index
799
Subject Index
804 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Reichl, Linda E. 1942- |
| author_GND | (DE-588)138557241 |
| author_facet | Reichl, Linda E. 1942- |
| author_role | aut |
| author_sort | Reichl, Linda E. 1942- |
| author_variant | l e r le ler |
| building | Verbundindex |
| bvnumber | BV021256461 |
| classification_rvk | UG 3500 |
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| ctrlnum | (OCoLC)255690068 (DE-599)BVBBV021256461 |
| discipline | Physik |
| discipline_str_mv | Physik |
| edition | 2. ed., [Nachdr.] |
| format | Book |
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| genre_facet | Lehrbuch |
| id | DE-604.BV021256461 |
| illustrated | Illustrated |
| index_date | 2024-07-02T13:40:43Z |
| indexdate | 2024-07-09T20:34:00Z |
| institution | BVB |
| isbn | 0471595209 9780471595205 |
| language | English |
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| physical | XIX, 822 S. Ill., graph. Darst. |
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| publisher | Wiley-VCH |
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| spelling | Reichl, Linda E. 1942- Verfasser (DE-588)138557241 aut A modern course in statistical physics L. E. Reichl 2. ed., [Nachdr.] Weinheim Wiley-VCH 2004 XIX, 822 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Thermodynamik (DE-588)4059827-5 gnd rswk-swf Statistische Mechanik (DE-588)4056999-8 gnd rswk-swf Statistische Thermodynamik (DE-588)4126251-7 gnd rswk-swf Statistische Physik (DE-588)4057000-9 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Statistische Physik (DE-588)4057000-9 s DE-604 Statistische Mechanik (DE-588)4056999-8 s Statistische Thermodynamik (DE-588)4126251-7 s 1\p DE-604 Thermodynamik (DE-588)4059827-5 s 2\p DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014577754&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Reichl, Linda E. 1942- A modern course in statistical physics Thermodynamik (DE-588)4059827-5 gnd Statistische Mechanik (DE-588)4056999-8 gnd Statistische Thermodynamik (DE-588)4126251-7 gnd Statistische Physik (DE-588)4057000-9 gnd |
| subject_GND | (DE-588)4059827-5 (DE-588)4056999-8 (DE-588)4126251-7 (DE-588)4057000-9 (DE-588)4123623-3 |
| title | A modern course in statistical physics |
| title_auth | A modern course in statistical physics |
| title_exact_search | A modern course in statistical physics |
| title_exact_search_txtP | A modern course in statistical physics |
| title_full | A modern course in statistical physics L. E. Reichl |
| title_fullStr | A modern course in statistical physics L. E. Reichl |
| title_full_unstemmed | A modern course in statistical physics L. E. Reichl |
| title_short | A modern course in statistical physics |
| title_sort | a modern course in statistical physics |
| topic | Thermodynamik (DE-588)4059827-5 gnd Statistische Mechanik (DE-588)4056999-8 gnd Statistische Thermodynamik (DE-588)4126251-7 gnd Statistische Physik (DE-588)4057000-9 gnd |
| topic_facet | Thermodynamik Statistische Mechanik Statistische Thermodynamik Statistische Physik Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014577754&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT reichllindae amoderncourseinstatisticalphysics |