Statistical Physics: Volume 1 of Modern Classical Physics
408
Statistical Physics: Volume 1 of Modern Classical Physics
408Paperback
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Overview
Kip Thorne and Roger Blandford’s monumental Modern Classical Physics is now available in five stand-alone volumes that make ideal textbooks for individual graduate or advanced undergraduate courses on statistical physics; optics; elasticity and fluid dynamics; plasma physics; and relativity and cosmology. Each volume teaches the fundamental concepts, emphasizes modern, real-world applications, and gives students a physical and intuitive understanding of the subject.
Statistical Physics is an essential introduction that is different from others on the subject because of its unique approach, which is coordinate-independent and geometric; embraces and elucidates the close quantum-classical connection and the relativistic and Newtonian domains; and demonstrates the power of statistical techniques—particularly statistical mechanics—by presenting applications not only to the usual kinds of things, such as gases, liquids, solids, and magnetic materials, but also to a much wider range of phenomena, including black holes, the universe, information and communication, and signal processing amid noise.
- Includes many exercise problems
- Features color figures, suggestions for further reading, extensive cross-references, and a detailed index
- Optional “Track 2” sections make this an ideal book for a one-quarter, half-semester, or full-semester course
- An online illustration package is available to professors
The five volumes, which are available individually as paperbacks and ebooks, are Statistical Physics; Optics; Elasticity and Fluid Dynamics; Plasma Physics; and Relativity and Cosmology.
Product Details
| ISBN-13: | 9780691206127 |
|---|---|
| Publisher: | Princeton University Press |
| Publication date: | 06/15/2021 |
| Pages: | 408 |
| Sales rank: | 859,986 |
| Product dimensions: | 8.00(w) x 10.00(h) x (d) |
About the Author
Table of Contents
List of Boxes xiii
Preface xv
Contents of Modern Classical Physics, volumes 1-5 xxi
Part I Foundations 1
1 Newtonian Physics: Geometric Viewpoint 5
1.1 Introduction 5
1.1.1 The Geometric Viewpoint on the Laws of Physics 5
1.1.2 Purposes of This Chapter 7
1.1.3 Overview of This Chapter 7
1.2 Foundational Concepts 8
1.3 Tensor Algebra without a Coordinate System 10
1.4 Particle Kinetics and Lorentz Force in Geometric Language 13
1.5 Component Representation of Tensor Algebra 16
1.5.1 Slot-Naming Index Notation 17
1.5.2 Particle Kinetics in Index Notation 19
1.6 Orthogonal Transformations of Bases 20
1.7 Differentiation of Scalars, Vectors, and Tensors; Cross Product and Curl 22
1.8 Volumes, Integration, and Integral Conservation Laws 26
1.8.1 Gauss's and Stokes' Theorems 27
1.9 The Stress Tensor and Momentum Conservation 29
1.9.1 Examples: Electromagnetic Field and Perfect Fluid 30
1.9.2 Conservation of Momentum 31
1.10 Geometrized Units and Relativistic Particles for Newtonian Readers 33
1.10.1 Geometrized Units 33
1.10.2 Energy and Momentum of a Moving Particle 34
Bibliographic Note 35
2 Special Relativity: Geometric Viewpoint T2 37
2.1 Overview 37
2.2 Foundational Concepts 38
2.2.1 Inertial Frames, Inertial Coordinates, Events, Vectors, and Spacetime Diagrams 38
2.2.2 The Principle of Relativity and Constancy of Light Speed 42
2.2.3 The Interval and Its Invariance 45
2.3 Tensor Algebra without a Coordinate System 48
2.4 Particle Kinetics and Lorentz Force without a Reference Frame 49
2.4.1 Relativistic Particle Kinetics: World Lines, 4-Velocity, 4-Momentum and Its Conservation, 4-Force 49
2.4.2 Geometric Derivation of the Lorentz Force Law 52
2.5 Component Representation of Tensor Algebra 54
2.5.1 Lorentz Coordinates 54
2.5.2 Index Gymnastics 54
2.5.3 Slot-Naming Notation 56
2.6 Particle Kinetics in Index Notation and in a Lorentz Frame 57
2.7 Lorentz Transformations 63
2.8 Spacetime Diagrams for Boosts 65
2.9 Time Travel 67
2.9.1 Measurement of Time; Twins Paradox 67
2.9.2 Wormholes 68
2.9.3 Wormhole as Time Machine 69
2.10 Directional Derivatives, Gradients, and the Levi-Civita Tensor 70
2.11 Nature of Electric and Magnetic Fields; Maxwell's Equations 71
2.12 Volumes, Integration, and Conservation Laws 75
2.12.1 Spacetime Volumes and Integration 75
2.12.2 Conservation of Charge in Spacetime 78
2.12.3 Conservation of Particles, Baryon Number, and Rest Mass 79
2.13 Stress-Energy Tensor and Conservation of 4-Momentum 82
2.13.1 Stress-Energy Tensor 82
2.13.2 4-Momentum Conservation 84
2.13.3 Stress-Energy Tensors for Perfect Fluids and Electromagnetic Fields 85
Bibliographic Note 88
Part II Statistical Physics 91
3 Kinetic Theory 95
3.1 Overview 95
3.2 Phase Space and Distribution Function 97
3.2.1 Newtonian Number Density in Phase Space, N 97
3.2.2 Relativistic Number Density in Phase Space, N 99
3.2.3 Distribution Function f(x, v, t) for Particles in a Plasma 105
3.2.4 Distribution Function Iv/v3 for Photons 106
3.2.5 Mean Occupation Number η 108
3.3 Thermal-Equilibrium Distribution Functions 111
3.4 Macroscopic Properties of Matter as Integrals over Momentum Space 117
3.4.1 Particle Density n, Flux S, and Stress Tensor T 117
3.4.2 Relativistic Number-Flux 4-Vector S and Stress-Energy Tensor T 118
3.5 Isotropic Distribution Functions and Equations of State 120
3.5.1 Newtonian Density, Pressure, Energy Density, and Equation of State 120
3.5.2 Equations of State for a Nonrelativistic Hydrogen Gas 122
3.5.3 Relativistic Density, Pressure, Energy Density, and Equation of State 125
3.5.4 Equation of State for a Relativistic Degenerate Hydrogen Gas 126
3.5.5 Equation of State for Radiation 128
3.6 Evolution of the Distribution Function: Liouville's Theorem, the Collisionless Boltzmann Equation, and the Boltzmann Transport Equation 132
3.7 Transport Coefficients 139
3.7.1 Diffusive Heat Conduction inside a Star 142
3.7.2 Order-of-Magnitude Analysis 143
3.7.3 Analysis Using the Boltzmann Transport Equation 144
Bibliographic Note 153
4 Statistical Mechanics 155
4.1 Overview 155
4.2 Systems, Ensembles, and Distribution Functions 157
4.2.1 Systems 157
4.2.2 Ensembles 160
4.2.3 Distribution Function 161
4.3 Liouville's Theorem and the Evolution of the Distribution Function 166
4.4 Statistical Equilibrium 168
4.4.1 Canonical Ensemble and Distribution 169
4.4.2 General Equilibrium Ensemble and Distribution; Gibbs Ensemble; Grand Canonical Ensemble 172
4.4.3 Fermi-Dirac and Bose-Einstein Distributions 174
4.4.4 Equipartition Theorem for Quadratic, Classical Degrees of Freedom 177
4.5 The Microcanonical Ensemble 178
4.6 The Ergodic Hypothesis 180
4.7 Entropy and Evolution toward Statistical Equilibrium 181
4.7.1 Entropy and the Second Law of Thermodynamics 181
4.7.2 What Causes the Entropy to Increase? 183
4.8 Entropy per Particle 191
4.9 Bose-Einstein Condensate 193
4.10 Statistical Mechanics in the Presence of Gravity 201
4.10.1 Galaxies 201
4.10.2 Black Holes 204
4.10.3 The Universe 209
4.10.4 Structure Formation in the Expanding Universe: Violent Relaxation and Phase Mixing 210
4.11 Entropy and Information 211
4.11.1 Information Gained When Measuring the State of a System in a Microcanonical Ensemble 211
4.11.2 Information in Communication Theory 212
4.11.3 Examples of Information Content 214
4.11.4 Some Properties of Information 216
4.11.5 Capacity of Communication Channels; Erasing Information from Computer Memories 216
Bibliographic Note 218
5 Statistical Thermodynamics 219
5.1 Overview 219
5.2 Microcanonical Ensemble and the Energy Representation of Thermodynamics 221
5.2.1 Extensive and Intensive Variables; Fundamental Potential 221
5.2.2 Energy as a Fundamental Potential 222
5.2.3 Intensive Variables Identified Using Measuring Devices; First Law of Thermodynamics 223
5.2.4 Euler's Equation and Form of the Fundamental Potential 226
5.2.5 Everything Deducible from First Law; Maxwell Relations 227
5.2.6 Representations of Thermodynamics 228
5.3 Grand Canonical Ensemble and the Grand-Potential Representation of Thermodynamics 229
5.3.1 The Grand-Potential Representation, and Computation of Thermodynamic Properties as a Grand Canonical Sum 229
5.3.2 Nonrelativistic van der Waals Gas 232
5.4 Canonical Ensemble and the Physical-Free-Energy Representation of Thermodynamics 239
5.4.1 Experimental Meaning of Physical Free Energy 241
5.4.2 Ideal Gas with Internal Degrees of Freedom 242
5.5 Gibbs Ensemble and Representation of Thermodynamics; Phase Transitions and Chemical Reactions 246
5.5.1 Out-of-Equilibrium Ensembles and Their Fundamental Thermodynamic Potentials and Minimum Principles 248
5.5.2 Phase Transitions 251
5.5.3 Chemical Reactions 256
5.6 Fluctuations away from Statistical Equilibrium 260
5.7 Van der Waals Gas: Volume Fluctuations and Gas-to-Liquid Phase Transition 266
5.8 Magnetic Materials 270
5.8.1 Paramagnetism; The Curie Law 271
5.8.2 Ferromagnetism: The Ising Model 272
5.8.3 Renormalization Group Methods for the Ising Model 273
5.8.4 Monte Carlo Methods for the Ising Model 279
Bibliographic Note 282
6 Random Processes 283
6.1 Overview 283
6.2 Fundamental Concepts 285
6.2.1 Random Variables and Random Processes 285
6.2.2 Probability Distributions 286
6.2.3 Ergodic Hypothesis 288
6.3 Markov Processes and Gaussian Processes 289
6.3.1 Markov Processes; Random Walk 289
6.3.2 Gaussian Processes and the Central Limit Theorem; Random Walk 292
6.3.3 Doob's Theorem for Gaussian-Markov Processes, and Brownian Motion 295
6.4 Correlation Functions and Spectral Densities 297
6.4.1 Correlation Functions; Proof of Doob's Theorem 297
6.4.2 Spectral Densities 299
6.4.3 Physical Meaning of Spectral Density, Light Spectra, and Noise in a Gravitational Wave Detector 301
6.4.4 The Wiener-Khintchine Theorem; Cosmological Density Fluctuations 303
6.5 2-Dimensional Random Processes 306
6.5.1 Cross Correlation and Correlation Matrix 306
6.5.2 Spectral Densities and the Wiener-Khintchine Theorem 307
6.6 Noise and Its Types of Spectra 308
6.6.1 Shot Noise, Flicker Noise, and Random-Walk Noise; Cesium Atomic Clock 308
6.6.2 Information Missing from Spectral Density 310
6.7 Filtering Random Processes 311
6.7.1 Filters, Their Kernels, and the Filtered Spectral Density 311
6.7.2 Brownian Motion and Random Walks 313
6.7.3 Extracting a Weak Signal from Noise: Band-Pass Filter, Wiener's Optimal Filter, Signal-to-Noise Ratio, and Allan Variance of Clock Noise 315
6.7.4 Shot Noise 321
6.8 Fluctuation-Dissipation Theorem 323
6.8.1 Elementary Version of the Fluctuation-Dissipation Theorem; Langevin Equation, Johnson Noise in a Resistor, and Relaxation Time for Brownian Motion 323
6.8.2 Generalized Fluctuation-Dissipation Theorem; Thermal Noise in a Laser Beam's Measurement of Mirror Motions; Standard Quantum Limit for Measurement Accuracy and How to Evade It 331
6.9 Fokker-Planck Equation 335
6.9.1 Fokker-Planck for a 1-Dimensional Markov Process 336
6.9.2 Optical Molasses: Doppler Cooling of Atoms 340
6.9.3 Fokker-Planck for a Multidimensional Markov Process; Thermal Noise in an Oscillator 343
Bibliographic Note 345
References 347
Name Index 353
Subject Index 355
Contents of the Unified Work, Modern Classical Physics 367
Preface to Modern Classical Physics 375
Acknowledgments for Modern Classical Physics 383
What People are Saying About This
“Extraordinarily impressive.”—Malcolm Longair, Nature“A magnificent achievement.”—Edward Witten, Physics Today