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目次

Preface xi Chapter 1: From Microscopic to Macroscopic Behavior 1 1.1Introduction 1 1.2 Some Qualitative Observations 2 1.3 Doing Work and theQuality of Energy 4 1.4 Some Simple Simulations 5 1.5 Measuring thePressure and Temperature 15 1.6 Work, Heating, and the First Law ofThermodynamics 19 1.7 *The Fundamental Need for a Statistical Approach 201.8 *Time and Ensemble Averages 22 1.9 Models of Matter 22 1.9.1 The idealgas 23 1.9.2 Interparticle potentials 23 1.9.3 Lattice models 23 1.10Importance of Simulations 24 1.11 Dimensionless Quantities 24 1.12 Summary25 1.13 Supplementary Notes 27 1.13.1 Approach to equilibrium 27 1.13.2Mathematics refresher 28 Vocabulary 28 Additional Problems 29 Suggestionsfor Further Reading 30 Chapter 2: Thermodynamic Concepts and Processes32 2.1 Introduction 32 2.2 The System 33 2.3 Thermodynamic Equilibrium 342.4 Temperature 35 2.5 Pressure Equation of State 38 2.6 Some ThermodynamicProcesses 39 2.7 Work 40 2.8 The First Law of Thermodynamics 44 2.9 EnergyEquation of State 47 2.10 Heat Capacities and Enthalpy 48 2.11 QuasistaticAdiabatic Processes 51 2.12 The Second Law of Thermodynamics 55 2.13 TheThermodynamic Temperature 58 2.14 The Second Law and Heat Engines 60 2.15Entropy Changes 67 2.16 Equivalence of Thermodynamic and Ideal Gas ScaleTemperatures 74 2.17 The Thermodynamic Pressure 75 2.18 The FundamentalThermodynamic Relation 76 2.19 The Entropy of an Ideal Classical Gas 772.20 The Third Law of Thermodynamics 78 2.21 Free Energies 79 2.22Thermodynamic Derivatives 84 2.23 *Applications to Irreversible Processes 902.23.1 Joule or free expansion process 90 2.23.2 Joule-Thomson process 912.24 Supplementary Notes 94 2.24.1 The mathematics of thermodynamics 942.24.2 Thermodynamic potentials and Legendre transforms 97 Vocabulary 99Additional Problems 100 Suggestions for Further Reading 108 Chapter 3:Concepts of Probability 111 3.1 Probability in Everyday Life 111 3.2 TheRules of Probability 114 3.3 Mean Values 119 3.4 The Meaning of Probability121 3.4.1 Information and uncertainty 124 3.4.2 *Bayesian inference 1283.5 Bernoulli Processes and the Binomial Distribution 134 3.6 ContinuousProbability Distributions 147 3.7 The Central Limit Theorem (or WhyThermodynamics Is Possible) 151 3.8 *The Poisson Distribution or Should YouFly? 155 3.9 *Traffic Flow and the Exponential Distribution 156 3.10 *AreAll Probability Distributions Gaussian? 159 3.11 Supplementary Notes 1613.11.1 Method of undetermined multipliers 161 3.11.2 Derivation of thecentral limit theorem 163 Vocabulary 167 Additional Problems 168Suggestions for Further Reading 177 Chapter 4: The Methodology ofStatistical Mechanics 180 4.1 Introduction 180 4.2 A Simple Example of aThermal Interaction 182 4.3 Counting Microstates 192 4.3.1 Noninteractingspins 192 4.3.2 A particle in a one-dimensional box 193 4.3.3One-dimensional harmonic oscillator 196 4.3.4 One particle in atwo-dimensional box 197 4.3.5 One particle in a three-dimensional box 1984.3.6 Two noninteracting identical particles and the semiclassical limit 1994.4 The Number of States of Many Noninteracting Particles: SemiclassicalLimit 201 4.5 The Microcanonical Ensemble (Fixed E, V, and N) 203 4.6 TheCanonical Ensemble (Fixed T, V, and N) 209 4.7 Connection betweenThermodynamics and Statistical Mechanics in the Canonical Ensemble 216 4.8Simple Applications of the Canonical Ensemble 218 4.9 An Ideal Thermometer222 4.10 Simulation of the Microcanonical Ensemble 225 4.11 Simulation ofthe Canonical Ensemble 226 4.12 Grand Canonical Ensemble (Fixed T, V, and ?)227 4.13 *Entropy Is Not a Measure of Disorder 229 4.14 Supplementary Notes231 4.14.1 The volume of a hypersphere 231 4.14.2 Fluctuations in thecanonical ensemble 232 Vocabulary 233 Additional Problems 234 Suggestionsfor Further Reading 239 Chapter 5: Magnetic Systems 241 5.1Paramagnetism 241 5.2 Noninteracting Magnetic Moments 242 5.3Thermodynamics of Magnetism 246 5.4 The Ising Model 248 5.5 The Ising Chain249 5.5.1 Exact enumeration 250 5.5.2 Spin-spin correlation function 2535.5.3 Simulations of the Ising chain 256 5.5.4 *Transfer matrix 257 5.5.5Absence of a phase transition in one dimension 260 5.6 The Two-DimensionalIsing Model 261 5.6.1 Onsager solution 262 5.6.2 Computer simulation of thetwo-dimensional Ising model 267 5.7 Mean-Field Theory 270 5.7.1 *Phasediagram of the Ising model 276 5.8 *Simulation of the Density of States 2795.9 *Lattice Gas 282 5.10 Supplementary Notes 286 5.10.1 The Heisenbergmodel of magnetism 286 5.10.2 Low temperature expansion 288 5.10.3 Hightemperature expansion 290 5.10.4 Bethe approximation 292 5.10.5 Fullyconnected Ising model 295 5.10.6 Metastability and nucleation 297Vocabulary 300 Additional Problems 300 Suggestions for Further Reading 306Chapter 6: Many-Particle Systems 308 6.1 The Ideal Gas in theSemiclassical Limit 308 6.2 Classical Statistical Mechanics 318 6.2.1 Theequipartition theorem 318 6.2.2 The Maxwell velocity distribution 321 6.2.3The Maxwell speed distribution 323 6.3 Occupation Numbers and Bose and FermiStatistics 325 6.4 Distribution Functions of Ideal Bose and Fermi Gases 3276.5 Single Particle Density of States 329 6.5.1 Photons 331 6.5.2Nonrelativistic particles 332 6.6 The Equation of State of an IdealClassical Gas: Application of the Grand Canonical Ensemble 334 6.7Blackbody Radiation 337 6.8 The Ideal Fermi Gas 341 6.8.1 Ground stateproperties 342 6.8.2 Low temperature properties 345 6.9 The Heat Capacityof a Crystalline Solid 351 6.9.1 The Einstein model 351 6.9.2 Debye theory352 6.10 The Ideal Bose Gas and Bose Condensation 354 6.11 SupplementaryNotes 360 6.11.1 Fluctuations in the number of particles 360 6.11.2 Lowtemperature expansion of an ideal Fermi gas 363 Vocabulary 365 AdditionalProblems 366 Suggestions for Further Reading 374 Chapter 7: TheChemical Potential and Phase Equilibria 376 7.1 Meaning of the ChemicalPotential 376 7.2 Measuring the Chemical Potential in Simulations 380 7.2.1The Widom insertion method 380 7.2.2 The chemical demon algorithm 382 7.3Phase Equilibria 385 7.3.1 Equilibrium conditions 386 7.3.2 Simple phasediagrams 387 7.3.3 Clausius-Clapeyron equation 389 7.4 The van der WaalsEquation of State 393 7.4.1 Maxwell construction 393 7.4.2 *The van derWaals critical point 400 7.5 *Chemical Reactions 403 Vocabulary 407Additional Problems 407 Suggestions for Further Reading 408 Chapter 8:Classical Gases and Liquids 410 8.1 Introduction 410 8.2 Density Expansion410 8.3 The Second Virial Coefficient 414 8.4 *Diagrammatic Expansions 4198.4.1 Cumulants 420 8.4.2 High temperature expansion 421 8.4.3 Densityexpansion 426 8.4.4 Higher order virial coefficients for hard spheres 4288.5 The Radial Distribution Function 430 8.6 Perturbation Theory of Liquids437 8.6.1 The van der Waals equation 439 8.7 *The Ornstein-Zernike Equationand Integral Equations for g(r ) 441 8.8 *One-Component Plasma 445 8.9Supplementary Notes 449 8.9.1 The third virial coefficient for hard spheres449 8.9.2 Definition of g(r ) in terms of the local particle density 4508.9.3 X-ray scattering and the static structure function 451 Vocabulary 455Additional Problems 456 Suggestions for Further Reading 458 Chapter 9:Critical Phenomena: Landau Theory and the Renormalization Group Method 4599.1 Landau Theory of Phase Transitions 459 9.2 Universality and ScalingRelations 467 9.3 A Geometrical Phase Transition 469 9.4 RenormalizationGroup Method for Percolation 475 9.5 The Renormalization Group Method andthe One-Dimensional Ising Model 479 9.6 ?The Renormalization Group Methodand the Two-Dimensional Ising Model 484 Vocabulary 490 Additional Problems491 Suggestions for Further Reading 492 Appendix: Physical Constantsand Mathematical Relations 495 A.1 Physical Constants and Conversion Factors495 A.2 Hyperbolic Functions 496 A.3 Approximations 496 A.4Euler-Maclaurin Formula 497 A.5 Gaussian Integrals 497 A.6 Stirling'sApproximation 498 A.7 Bernoulli Numbers 500 A.8 Probability Distributions500 A.9 Fourier Transforms 500 A.10 The Delta Function 501 A.11Convolution Integrals 502 A.12 Fermi and Bose Integrals 503 Index 505