Statistical Physics

Kip S. Thorne, winner of the Nobel Prize in physics, is the Feynman Professor Emeritus of Theoretical Physics at Caltech. His books include Gravitation (Princeton) and Black Holes and Time Warps: Einstein’s Outrageous Legacy. Roger D. Blandford, winner of the Crafoord and Shaw prizes in astronomy, is the Luke Blossom Professor in the School of Humanities and Sciences and founding director of the Kavli Institute for Particle Astrophysics and Cosmology at Stanford University.

"Kip S. Thorne, Co-Winner of the 2017 Nobel Prize in Physics"

• List of BoxesPrefaceContents of Modern Classical Physics, volumes 1–5PART I FOUNDATIONS1 Newtonian Physics: Geometric Viewpoint1.1 Introduction1.1.1 The Geometric Viewpoint on the Laws of Physics1.1.2 Purposes of This Chapter1.1.3 Overview of This Chapter1.2 Foundational Concepts1.3 Tensor Algebra without a Coordinate System1.4 Particle Kinetics and Lorentz Force in Geometric Language1.5 Component Representation of Tensor Algebra1.5.1 Slot-Naming Index Notation1.5.2 Particle Kinetics in Index Notation1.6 Orthogonal Transformations of Bases1.7 Differentiation of Scalars, Vectors, and Tensors; Cross Product and Curl1.8 Volumes, Integration, and Integral Conservation Laws1.8.1 Gauss’s and Stokes’ Theorems1.9 The Stress Tensor and Momentum Conservation1.9.1 Examples: Electromagnetic Field and Perfect Fluid1.9.2 Conservation of Momentum1.10 Geometrized Units and Relativistic Particles for Newtonian Readers1.10.1 Geometrized Units1.10.2 Energy and Momentum of a Moving ParticleBibliographic Note2 Special Relativity: Geometric Viewpoint2.1 Overview2.2 Foundational Concepts2.2.1 Inertial Frames, Inertial Coordinates, Events, Vectors, and Spacetime Diagrams2.2.2 The Principle of Relativity and Constancy of Light Speed2.2.3 The Interval and Its Invariance2.3 Tensor Algebra without a Coordinate System2.4 Particle Kinetics and Lorentz Force without a Reference Frame2.4.1 Relativistic Particle Kinetics: World Lines, 4-Velocity, 4-Momentum and Its Conservation, 4-Force2.4.2 Geometric Derivation of the Lorentz Force Law2.5 Component Representation of Tensor Algebra2.5.1 Lorentz Coordinates2.5.2 Index Gymnastics2.5.3 Slot-Naming Notation2.6 Particle Kinetics in Index Notation and in a Lorentz Frame2.7 Lorentz Transformations2.8 Spacetime Diagrams for Boosts2.9 Time Travel2.9.1 Measurement of Time; Twins Paradox2.9.2 Wormholes2.9.3 Wormhole as Time Machine2.10 Directional Derivatives, Gradients, and the Levi-Civita Tensor2.11 Nature of Electric and Magnetic Fields; Maxwell’s Equations2.12 Volumes, Integration, and Conservation Laws2.12.1 Spacetime Volumes and Integration2.12.2 Conservation of Charge in Spacetime2.12.3 Conservation of Particles, Baryon Number, and Rest Mass2.13 Stress-Energy Tensor and Conservation of 4-Momentum2.13.1 Stress-Energy Tenso2.13.2 4-Momentum Conservation2.13.3 Stress-Energy Tensors for Perfect Fluids and Electromagnetic FieldsBibliographic NotePART II STATISTICAL PHYSICS3 Kinetic Theory3.1 Overview3.2 Phase Space and Distribution Function3.2.1 Newtonian Number Density in Phase Space, 𝒩3.2.2 Relativistic Number Density in Phase Space, 𝒩3.2.3 Distribution Function ƒ (x, v, t) for Particles in a Plasma3.2.4 Distribution Function Iⱱ/ⱱ3 for Photons3.2.5 Mean Occupation Number ƞ3.3 Thermal-Equilibrium Distribution Functions3.4 Macroscopic Properties of Matter as Integrals over Momentum Space3.4.1 Particle Density n, Flux S, and Stress Tensor ⊤3.4.2 Relativistic Number-Flux 4-Vector S→ and Stress-Energy Tensor ⊤3.5 Isotropic Distribution Functions and Equations of State3.5.1 Newtonian Density, Pressure, Energy Density, and Equation of State3.5.2 Equations of State for a Nonrelativistic Hydrogen Gas3.5.3 Relativistic Density, Pressure, Energy Density, and Equation of State3.5.4 Equation of State for a Relativistic Degenerate Hydrogen Gas3.5.5 Equation of State for Radiation3.6 Evolution of the Distribution Function: Liouville’s Theorem, the Collisionless Boltzmann Equation, and the Boltzmann Transport Equation3.7 Transport Coefficients3.7.1 Diffusive Heat Conduction inside a Star3.7.2 Order-of-Magnitude Analysis3.7.3 Analysis Using the Boltzmann Transport EquationBibliographic Note4 Statistical Mechanics4.1 Overview4.2 Systems, Ensembles, and Distribution Functions4.2.1 Systems4.2.2 Ensembles4.2.3 Distribution Function4.3 Liouville’s Theorem and the Evolution of the Distribution Function4.4 Statistical Equilibrium4.4.1 Canonical Ensemble and Distribution4.4.2 General Equilibrium Ensemble and Distribution; Gibbs Ensemble Grand Canonical Ensemble4.4.3 Fermi-Dirac and Bose-Einstein Distributions4.4.4 Equipartition Theorem for Quadratic, Classical Degrees of Freedom4.5 The Microcanonical Ensemble4.6 The Ergodic Hypothesis4.7 Entropy and Evolution toward Statistical Equilibrium4.7.1 Entropy and the Second Law of Thermodynamics4.7.2 What Causes the Entropy to Increase?4.8 Entropy per Particle4.9 Bose-Einstein Condensate4.10 Statistical Mechanics in the Presence of Gravity4.10.1 Galaxies4.10.2 Black Holes4.10.3 The Universe4.10.4 Structure Formation in the Expanding Universe: Violent Relaxation and Phase Mixing4.11 Entropy and Information4.11.1 Information Gained When Measuring the State of a System in a Microcanonical Ensemble4.11.2 Information in Communication Theory4.11.3 Examples of Information Content4.11.4 Some Properties of Information4.11.5 Capacity of Communication Channels; Erasing Information from Computer MemoriesBibliographic Note5 Statistical Thermodynamics5.1 Overview5.2 Microcanonical Ensemble and the Energy Representation of Thermodynamics5.2.1 Extensive and Intensive Variables; Fundamental Potential5.2.2 Energy as a Fundamental Potential5.2.3 Intensive Variables Identified Using Measuring Devices First Law of Thermodynamics5.2.4 Euler’s Equation and Form of the Fundamental Potential5.2.5 Everything Deducible from First Law; Maxwell Relations5.2.6 Representations of Thermodynamics5.3 Grand Canonical Ensemble and the Grand-Potential Representation of Thermodynamics5.3.1 The Grand-Potential Representation, and Computation of Thermodynamic Properties as a Grand Canonical Sum5.3.2 Nonrelativistic van der Waals Gas5.4 Canonical Ensemble and the Physical-Free-Energy Representation of Thermodynamics5.4.1 Experimental Meaning of Physical Free Energy5.4.2 Ideal Gas with Internal Degrees of Freedom5.5 Gibbs Ensemble and Representation of Thermodynamics; Phase Transitions and Chemical Reactions5.5.1 Out-of-Equilibrium Ensembles and Their Fundamental Thermodynamic Potentials and Minimum Principles5.5.2 Phase Transitions5.5.3 Chemical Reactions5.6 Fluctuations away from Statistical Equilibrium5.7 Van der Waals Gas: Volume Fluctuations and Gas-to-Liquid Phase Transition5.8 Magnetic Materials5.8.1 Paramagnetism; The Curie Law5.8.2 Ferromagnetism: The Ising Model5.8.3 Renormalization Group Methods for the Ising Model5.8.4 Monte Carlo Methods for the Ising ModelBibliographic Note6 Random Processes6.1 Overview6.2 Fundamental Concepts6.2.1 Random Variables and Random Processes6.2.2 Probability Distributions6.2.3 Ergodic Hypothesis6.3 Markov Processes and Gaussian Processes6.3.1 Markov Processes; Random Walk6.3.2 Gaussian Processes and the Central Limit Theorem; Random Walk6.3.3 Doob’s Theorem for Gaussian-Markov Processes, and Brownian Motion6.4 Correlation Functions and Spectral Densities6.4.1 Correlation Functions; Proof of Doob’s Theorem6.4.2 Spectral Densities6.4.3 Physical Meaning of Spectral Density, Light Spectra, and Noise in a Gravitational Wave Detector6.4.4 The Wiener-Khintchine Theorem; Cosmological Density Fluctuations6.5 2-Dimensional Random Processes6.5.1 Cross Correlation and Correlation Matrix6.5.2 Spectral Densities and the Wiener-Khintchine Theorem6.6 Noise and Its Types of Spectra6.6.1 Shot Noise, Flicker Noise, and Random-Walk Noise; Cesium Atomic Clock6.6.2 Information Missing from Spectral Density6.7 Filtering Random Processes6.7.1 Filters, Their Kernels, and the Filtered Spectral Density6.7.2 Brownian Motion and Random Walks6.7.3 Extracting a Weak Signal from Noise: Band-Pass Filter, Wiener’s Optimal Filter Signal-to-Noise Ratio, and Allan Variance of Clock Noise6.7.4 Shot Noise6.8 Fluctuation-Dissipation Theorem6.8.1 Elementary Version of the Fluctuation-Dissipation Theorem; Langevin Equation Johnson Noise in a Resistor, and Relaxation Time for Brownian Motion6.8.2 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 It6.9 Fokker-Planck Equation6.9.1 Fokker-Planck for a 1-Dimensional Markov Process6.9.2 Optical Molasses: Doppler Cooling of Atoms6.9.3 Fokker-Planck for a Multidimensional Markov Process; Thermal Noise in an OscillatorBibliographic NoteReferencesName IndexSubject IndexContents of the Unified Work, Modern Classical PhysicsPreface to Modern Classical PhysicsAcknowledgments for Modern Classical Physics