Statistical and Thermal Physics : With Computer Applications

by Gould, Harvey; Tobochnik, Jan

• ISBN13: 9781400837038
• ISBN10: 1400837030
• Format: Hardcover
• Copyright: 2010-08-19
• Publisher: PRINCETON UNIVERSITY PRESS

Summary

This textbook carefully develops the main ideas and techniques of statistical and thermal physics and is intended for upper-level undergraduate courses. The authors each have more than thirty years' experience in teaching, curriculum development, and research in statistical and computational physics.Statistical and Thermal Physicsbegins with a qualitative discussion of the relation between the macroscopic and microscopic worlds and incorporates computer simulations throughout the book to provide concrete examples of important conceptual ideas. Unlike many contemporary texts on thermal physics, this book presents thermodynamic reasoning as an independent way of thinking about macroscopic systems. Probability concepts and techniques are introduced, including topics that are useful for understanding how probability and statistics are used. Magnetism and the Ising model are considered in greater depth than in most undergraduate texts, and ideal quantum gases are treated within a uniform framework. Advanced chapters on fluids and critical phenomena are appropriate for motivated undergraduates and beginning graduate students. Integrates Monte Carlo and molecular dynamics simulations as well as other numerical techniques throughout the text Provides self-contained introductions to thermodynamics and statistical mechanics Discusses probability concepts and methods in detail Contains ideas and methods from contemporary research Includes advanced chapters that provide a natural bridge to graduate study Features more than 400 problems Programs are open source and available in an executable cross-platform format Solutions manual (available only to teachers)

Table of Contents

Preface	p. xi
From Microscopic to Macroscopic Behavior	p. 1
Introduction	p. 1
Some Qualitative Observations	p. 2
Doing Work and the Quality of Energy	p. 4
Some Simple Simulations	p. 5
Measuring the Pressure and Temperature	p. 15
Work, Heating, and the First Law of Thermodynamics	p. 19
*The Fundamental Need for a Statistical Approach	p. 20
*Time and Ensemble Averages	p. 22
Models of Matter	p. 22
The ideal gas	p. 23
Interparticle potentials	p. 23
Lattice models	p. 23
Importance of Simulations	p. 24
Dimensionless Quantities	p. 24
Summary	p. 25
Supplementary Notes	p. 27
Approach to equilibrium	p. 27
Mathematics refresher	p. 28
Vocabulary	p. 28
Additional Problems	p. 29
Suggestions for Further Reading	p. 30
Thermodynamic Concepts and Processes	p. 32
Introduction	p. 32
The System	p. 33
Thermodynamic Equilibrium	p. 34
Temperature	p. 35
Pressure Equation of State	p. 38
Some Thermodynamic Processes	p. 39
Work	p. 40
The First Law of Thermodynamics	p. 44
Energy Equation of State	p. 47
Heat Capacities and Enthalpy	p. 48
Quasistatic Adiabatic Processes	p. 51
The Second Law of Thermodynamics	p. 55
The Thermodynamic Temperature	p. 58
The Second Law and Heat Engines	p. 60
Entropy Changes	p. 67
Equivalence of Thermodynamic and Ideal Gas Scale Temperatures	p. 74
The Thermodynamic Pressure	p. 75
The Fundamental Thermodynamic Relation	p. 76
The Entropy of an Ideal Classical Gas	p. 77
The Third Law of Thermodynamics	p. 78
Free Energies	p. 79
Thermodynamic Derivatives	p. 84
*Applications to Irreversible Processes	p. 90
Joule or free expansion process	p. 90
Joule-Thomson process	p. 91
Supplementary Notes	p. 94
The mathematics of thermodynamics	p. 94
Thermodynamic potentials and Legendre transforms	p. 97
Vocabulary	p. 99
Additional Problems	p. 100
Suggestions for Further Reading	p. 108
Concepts of Probability	p. 111
Probability in Everyday Life	p. 111
The Rules of Probability	p. 114
Mean Values	p. 119
The Meaning of Probability	p. 121
Information and uncertainty	p. 124
*Bayesian inference	p. 128
Bernoulli Processes and the Binomial Distribution	p. 134
Continuous Probability Distributions	p. 147
The Central Limit Theorem (or Why Thermodynamics Is Possible)	p. 151
*The Poisson Distribution or Should You Fly?	p. 155
*Traffic Flow and the Exponential Distribution	p. 156
*Are All Probability Distributions Gaussian?	p. 159
Supplementary Notes	p. 161
Method of undetermined multipliers	p. 161
Derivation of the central limit theorem	p. 163
Vocabulary	p. 167
Additional Problems	p. 168
Suggestions for Further Reading	p. 177
The Methodology of Statistical Mechanics	p. 180
Introduction	p. 180
A Simple Example of a Thermal Interaction	p. 182
Counting Microstates	p. 192
Noninteracting spins	p. 192
A particle in a one-dimensional box	p. 193
One-dimensional harmonic oscillator	p. 196
One particle in a two-dimensional box	p. 197
One particle in a three-dimensional box	p. 198
Two noninteracting identical particles and the semiclassical limit	p. 199
The Number of States of Many Noninteracting Particles: Semiclassical Limit	p. 201
The Microcanonical Ensemble (Fixed E, V, and N)	p. 203
The Canonical Ensemble (Fixed T, V, and N)	p. 209
Connection between Thermodynamics and Statistical Mechanics in the Canonical Ensemble	p. 216
Simple Applications of the Canonical Ensemble	p. 218
An Ideal Thermometer	p. 222
Simulation of the Microcanonical Ensemble	p. 225
Simulation of the Canonical Ensemble	p. 226
Grand Canonical Ensemble (Fixed T, V, and ?)	p. 227
*Entropy Is Not a Measure of Disorder	p. 229
Supplementary Notes	p. 231
The volume of a hypersphere	p. 231
Fluctuations in the canonical ensemble	p. 232
Vocabulary	p. 233
Additional Problems	p. 234
Suggestions for Further Reading	p. 239
Magnetic Systems	p. 241
Paramagnetism	p. 241
Noninteracting Magnetic Moments	p. 242
Thermodynamics of Magnetism	p. 246
The Ising Model	p. 248
The Ising Chain	p. 249
Exact enumeration	p. 250
Spin-spin correlation function	p. 253
Simulations of the Ising chain	p. 256
*Transfer matrix	p. 257
Absence of a phase transition in one dimension	p. 260
The Two-Dimensional Ising Model	p. 261
Onsager solution	p. 262
Computer simulation of the two-dimensional Ising model	p. 267
Mean-Field Theory	p. 270
*Phase diagram of the Ising model	p. 276
*Simulation of the Density of States	p. 279
*Lattice Gas	p. 282
Supplementary Notes	p. 286
The Heisenberg model of magnetism	p. 286
Low temperature expansion	p. 288
High temperature expansion	p. 290
Bethe approximation	p. 292
Fully connected Ising model	p. 295
Metastability and nucleation	p. 297
Vocabulary	p. 300
Additional Problems	p. 300
Suggestions for Further Reading	p. 306
Many-Particle Systems	p. 308
The Ideal Gas in the Semiclassical Limit	p. 308
Classical Statistical Mechanics	p. 318
The equipartition theorem	p. 318
The Maxwell velocity distribution	p. 321
The Maxwell speed distribution	p. 323
Occupation Numbers and Bose and Fermi Statistics	p. 325
Distribution Functions of Ideal Bose and Fermi Gases	p. 327
Single Particle Density of States	p. 329
Photons	p. 331
Nonrelativistic particles	p. 332
The Equation of State of an Ideal Classical Gas: Application of the Grand Canonical Ensemble	p. 334
Blackbody Radiation	p. 337
The Ideal Fermi Gas	p. 341
Ground state properties	p. 342
Low temperature properties	p. 345
The Heat Capacity of a Crystalline Solid	p. 351
The Einstein model	p. 351
Debye theory	p. 352
The Ideal Bose Gas and Bose Condensation	p. 354
Supplementary Notes	p. 360
Fluctuations in the number of particles	p. 360
Low temperature expansion of an ideal Fermi gas	p. 363
Vocabulary	p. 365
Additional Problems	p. 366
Suggestions for Further Reading	p. 374
The Chemical Potential and Phase Equilibria	p. 376
Meaning of the Chemical Potential	p. 376
Measuring the Chemical Potential in Simulations	p. 380
The Widom insertion method	p. 380
The chemical demon algorithm	p. 382
Phase Equilibria	p. 385
Equilibrium conditions	p. 386
Simple phase diagrams	p. 387
Clausius-Clapeyron equation	p. 389
The van der Waals Equation of State	p. 393
Maxwell construction	p. 393
*The van der Waals critical point	p. 400
*Chemical Reactions	p. 403
Vocabulary	p. 407
Additional Problems	p. 407
Suggestions for Further Reading	p. 408
Classical Gases and Liquids	p. 410
Introduction	p. 410
Density Expansion	p. 410
The Second Virial Coefficient	p. 414
*Diagrammatic Expansions	p. 419
Cumulants	p. 420
High temperature expansion	p. 421
Density expansion	p. 426
Higher order virial coefficients for hard spheres	p. 428
The Radial Distribution Function	p. 430
Perturbation Theory of Liquids	p. 437
The van der Waals equation	p. 439
*The Ornstein-Zernike Equation and Integral Equations for g(r )	p. 441
*One-Component Plasma	p. 445
Supplementary Notes	p. 449
The third virial coefficient for hard spheres	p. 449
Definition of g(r ) in terms of the local particle density	p. 450
X-ray scattering and the static structure function	p. 451
Vocabulary	p. 455
Additional Problems	p. 456
Suggestions for Further Reading	p. 458
Critical Phenomena: Landau Theory and the Renormalization Group Method	p. 459
Landau Theory of Phase Transitions	p. 459
Universality and Scaling Relations	p. 467
A Geometrical Phase Transition	p. 469
Renormalization Group Method for Percolation	p. 475
The Renormalization Group Method and the One-Dimensional Ising Model	p. 479
?The Renormalization Group Method and the Two-Dimensional Ising Model	p. 484
Vocabulary	p. 490
Additional Problems	p. 491
Suggestions for Further Reading	p. 492
Appendix: Physical Constants and Mathematical Relations	p. 495
Physical Constants and Conversion Factors	p. 495
Hyperbolic Functions	p. 496
Approximations	p. 496
Euler-Maclaurin Formula	p. 497
Gaussian Integrals	p. 497
Stirling's Approximation	p. 498
Bernoulli Numbers	p. 500
Probability Distributions	p. 500
Fourier Transforms	p. 500
The Delta Function	p. 501
Convolution Integrals	p. 502
Fermi and Bose Integrals	p. 503
Index	p. 505
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