Statistical and Thermal Physics: With Computer Applications, Second Edition

by Harvey Gould, Jan Tobochnik

Overview

A completely revised edition that combines a comprehensive coverage of statistical and thermal physics with enhanced computational tools, accessibility, and active learning activities to meet the needs of today's students and educators

This revised and expanded edition of Statistical and Thermal Physics introduces students to the essential ideas and techniques used in many areas of contemporary physics. Ready-to-run programs help make the many abstract concepts concrete. The text requires only a background in introductory mechanics and some basic ideas of quantum theory, discussing material typically found in undergraduate texts as well as topics such as fluids, critical phenomena, and computational techniques, which serve as a natural bridge to graduate study.

• Completely revised to be more accessible to students
• Encourages active reading with guided problems tied to the text
• Updated open source programs available in Java, Python, and JavaScript
• Integrates Monte Carlo and molecular dynamics simulations and other numerical techniques
• Self-contained introductions to thermodynamics and probability, including Bayes' theorem
• A fuller discussion of magnetism and the Ising model than other undergraduate texts
• Treats ideal classical and quantum gases within a uniform framework
• Features a new chapter on transport coefficients and linear response theory
• Draws on findings from contemporary research
• Solutions manual (available only to instructors)

Product Details

ISBN-13:	9780691201894
Publisher:	Princeton University Press
Publication date:	09/14/2021
Edition description:	School ed.
Pages:	528
Product dimensions:	7.00(w) x 10.00(h) x (d)

About the Author

Harvey Gould is Professor Emeritus of Physics at Clark University. Jan Tobochnik is the Dow Distinguished Professor of Natural Science at Kalamazoo College. They are the coauthors, with Wolfgang Christian, of An Introduction to Computer Simulation Methods: Applications to Physical Systems.

Table of Contents

Preface xi

Updated Preface to the First Edition xv

Links to Programs xxi

1 From Microscopic to Macroscopic Behavior 1

1.1 Introduction 1

1.2 Some Qualitative Observations 2

1.3 Doing Work and the Quality of Energy 4

1.4 Thermal Equilibrium 5

1.4.1 A probabilistic model 8

1.4.2 Counting states 10

1.4.3 Some qualitative observations 12

1.5 Measuring the Pressure and Temperature 13

1.6 Work, Heating, and the First Law of Thermodynamics 17

1.7 *The Fundamental Need for a Statistical Approach 18

1.8 *Time and Ensemble Averages 20

1.9 Phase Changes and Cooperative Effects 20

1.10 Models of Matter 21

1.10.1 The ideal gas 22

1.10.2 Interparticle potentials 22

1.10.3 Lattice models 22

1.11 Importance of Simulations 23

1.12 Dimensionless Quantities 23

1.13 Summary 24

1.14 Supplementary Notes 25

1.14.1 Approach to equilibrium 25

1.14.2 Mathematics refresher 26

Vocabulary 27

Additional Problems 27

Suggestions for Further Reading 28

2 Thermodynamic Concepts and Processes 30

2.1 Introduction 30

2.2 The System 31

2.3 Thermodynamic Equilibrium 31

2.4 Temperature 33

2.5 Pressure Equation of State 35

2.6 Some Thermodynamic Processes 37

2.7 Work 38

2.8 The First Law of Thermodynamics 41

2.9 Energy Equation of State 43

2.10 Heat Capacities and Enthalpy 44

2.11 Quasistatic Adiabatic Processes 47

2.12 The Second Law of Thermodynamics 51

2.13 The Thermodynamic Temperature 53

2.14 The Second Law and Heat Engines 55

2.15 Entropy Changes 63

2.16 Equivalence of Thermodynamic and Ideal Gas Scale Temperatures 67

2.17 The Thermodynamic Pressure 68

2.18 The Fundamental Thermodynamic Relation 69

2.19 The Entropy of an Ideal Classical Gas 71

2.20 The Third Law of Thermodynamics 71

2.21 Thermodynamic Potentials 72

2.22 Thermodynamic Derivatives 77

2.23 Applications to Irreversible Processes 82

2.23.1 Joule or free expansion process 82

2.23.2 Joule-Thomson process 84

2.24 Supplementary Notes 86

2.24.1 The mathematics of thermodynamics 86

2.24.2 Thermodynamic potentials and Legendre transforms 89

Vocabulary 92

Additional Problems 92

Suggestions for Further Reading 101

3 Concepts of Probability 104

3.1 Probability in Everyday Life 104

3.2 The Rules of Probability 107

3.3 Mean Values 110

3.4 The Meaning of Probability 112

3.4.1 Information and uncertainty 115

3.4.2 *Bayesian inference 119

3.5 Bernoulli Processes and the Binomial Distribution 124

3.6 Continuous Probability Distributions 137

3.7 The Central Limit Theorem (or Why Thermodynamics Is Possible) 140

3.8 *The Poisson Distribution 144

3.9 *Are All Probability Distributions Gaussian? 148

3.10 Supplementary Notes 150

3.10.1 Method of undetermined multipliers 150

3.10.2 Derivation of the central limit theorem 152

Vocabulary 156

Additional Problems 156

Suggestions for Further Reading 165

4 Methodology of Statistical Mechanics 167

4.1 Introduction 167

4.2 A Simple Example of a Thermal Interaction 169

4.3 Counting Microstates 177

4.3.1 Noninteracting spins 178

4.3.2 Harmonic oscillator 178

4.3.3 One particle in a one-dimensional box 180

4.3.4 One particle in a two-dimensional box 182

4.3.5 One particle in a three-dimensional box 183

4.3.6 Two noninteracting identical particles and the semiclassical limit 184

4.4 The Number of States of Many Noninteracting Particles: Semiclassical Limit 186

4.5 The Microcanonical Ensemble (Fixed E, V, and N) 187

4.6 The Canonical Ensemble (Fixed T, V, and N) 192

4.7 Simple Applications of the Canonical Ensemble 200

4.8 Grand Canonical Ensemble (Fixed T, V, and μ) 203

4.9 The Demon and the Boltzmarm Distribution 205

4.10 Simulation of the Microcanonical Ensemble 208

4.11 Simulation of the Canonical Ensemble 208

4.12 *Entropy Is Not a Measure of Disorder 210

4.13 Supplementary Notes 211

4.13.1 Number of microstates of the Einstein solid 211

4.13.2 The volume of a hypersphere 212

4.13.3 Fluctuations in the canonical ensemble 213

Vocabulary 214

Additional Problems 214

Suggestions for Further Reading 219

5 Magnetic Systems 221

5.1 Introduction 221

5.2 Thermodynamics of Magnetism 221

5.3 Noninteracting Magnetic Moments 221

5.4 The Ising Model 227

5.5 The Ising Chain 229

5.5.1 Exact enumeration 229

5.5.2 Spin-spin correlation function 232

5.5.3 Simulation of the Ising chain 234

5.5.4 Transfer matrix 235

5.5.5 Absence of a phase transition in one dimension 238

5.6 The Two-Dimensional Ising Model 239

5.6.1 Onsager solution 239

5.6.2 Computer simulation of the two-dimensional Ising model 244

5.7 Mean-Field Theory 245

5.7.1 *Phase diagram of the Ising model 251

5.8 *Simulation of the Number of States 253

5.9 Metastability and Nucleation 257

5.10 Supplementary Notes 259

5.10.1 Derivation of C(r) in one dimension 259

5.10.2 Lattice gas 261

5.10.3 The Heisenberg model of magnetism 264

5.10.4 Low temperature expansion 266

5.10.5 High temperature expansion 268

Vocabulary 270

Additional Problems 270

Suggestions for Further Reading 278

6 Many-Particle Systems 280

6.1 The Ideal Gas in the Semiclassical Limit 280

6.2 Classical Statistical Mechanics 289

6.2.1 The equipartition theorem 290

6.2.2 The Maxwell velocity distribution 292

6.3 Occupation Numbers and Bose and Fermi Statistics 295

6.4 Quantum Ideal Gases in the Grand Canonical Ensemble 297

6.5 Distribution Functions of Ideal Bose and Fermi Gases 298

6.6 Single Particle Density of States 299

6.6.1 Photons 301

6.6.2 Nonrelativistic particles 302

6.7 The Equation of State of an Ideal Classical Gas: Application of the Grand Canonical Ensemble 303

6.8 Blackbody Radiation 306

6.9 The Ideal Fermi Gas 309

6.9.1 Ground state properties 309

6.9.2 Low temperature properties 312

6.10 The Heat Capacity of a Crystalline Solid 314

6.10.1 The Einstein solid 315

6.10.2 Debye model 316

6.11 The Ideal Bose Gas and Bose-Einstein Condensation 318

6.12 Supplementary Notes 323

6.12.1 Fluctuations in the number of particles 323

6.12.2 Low temperature expansion of an ideal Fermi gas 326

Vocabulary 328

Additional Problems 329

Suggestions for Further Reading 339

7 The Chemical Potential and Phase Equilibria 340

7.1 Meaning of the Chemical Potential 340

7.2 Measuring the Chemical Potential in Simulations 344

7.3 Phase Equilibria 346

7.3.1 Equilibrium conditions 347

7.3.2 Simple phase diagrams 347

7.3.3 Clausius-Clapeyron equation 349

7.4 The van der Waals Equation of State 353

7.4.1 Maxwell construction 358

7.4.2 *Mean-field exponents and the van der Waals critical point 361

7.5 Chemical Reactions 363

7.6 Supplementary Notes: A demon with two sacks 366

Vocabulary 369

Additional Problems 369

Suggestions for Further Reading 370

8 Classical Gases and Liquids 372

8.1 Density Expansion 372

8.2 The Second Virial Coefficient 376

8.3 *Diagrammatic Expansions 381

8.3.1 Cumulants 381

8.3.2 High temperature expansion 382

8.3.3 Density expansion 387

8.3.4 Higher order virial coefficients for hard spheres 389

8.4 The Radial Distribution Function 391

8.5 Perturbation Theory of Liquids 398

8.5.1 The van der Waals equation 400

8.6 *The Ornstein-Zernike Equation and Integral Equations for g(r) 402

8.7 *One-Component Plasma 405

8.8 Supplementary Notes 409

8.8.1 The third virial coefficient for hard spheres 409

8.8.2 Definition of g(r) in terms of the local particle density 410

8.8.3 X-ray scattering and the static structure function 411

8.8.4 Compressibility equation 414

Vocabulary 415

Additional Problems 416

Suggestions for Further Reading 417

9 Critical Phenomena: Landau Theory and the Renormalization Group Method 419

9.1 Landau Theory of Phase Transitions 419

9.2 Universality and Scaling Relations 427

9.3 A Geometrical Phase Transition 429

9.4 Renormalization Group Method for Percolation 434

9.5 The Renormalization Group and the Ising Model in One Dimension 438

9.6 *The Renormalization Group and the Ising Model in Two Dimensions 441

9.7 Supplementary Notes: Decimation 445

Vocabulary 447

Additional Problems 447

Suggestions for Further Reading 449

10 It Is About Time: Time-Dependent Phenomena 451

10.1 Random Walks and Self-Diffusion 451

10.2 The Diffusion Equation 453

10.3 The Velocity Autocorrelation Function 455

10.4 Kinetic Theory of a Dilute Gas 456

10.5 Thermal Conductivity 461

10.6 Viscosity 465

10.7 The Langevin Equation and the Fluctuation-Dissipation Theorem 469

10.8 Linear Response 471

10.9 What If We Had More Time? 474

Supplementary Notes 475

10.9.1 Solution of the diffusion equation 475

10.9.2 Relation of the self-diffusion coefficient to the velocity autocorrelation function 477

10.9.3 The Boltzmann equation 478

10.9.4 More on linear response theory 480

Vocabulary 481

Additional Problems 481

Suggestions for Further Reading 483

Appendix: Physical Constants and Mathematical Relations 485

A.1 Physical Constants and Conversion Factors 485

A.2 Hyperbolic Functions 486

A.3 Approximations 486

A.4 Euler-Maclaurin Formula 487

A.5 Gaussian Integrals 487

A.6 Stirling's Approximation 488

A.7 Bernoulli Numbers 490

A.8 Probability Distributions 490

A.9 Fourier Transforms 490

A.10 The Delta Function 491

A.11 Convolution Integrals 492

A.12 Fermi and Bose Integrals 493

Index 495

What People are Saying About This

From the Publisher

"A remarkable textbook, Statistical and Thermal Physics . . . is sure to rapidly become a classic in this field. As opposed to some textbooks, that expose and develop the two disciplines in tandem, Gould and Tobochnik discuss Thermodynamics first and only then broach the subject of Statistical Mechanics, minimizing the confusion that arises from shifting back and forth between the two main story lines."—Daniel ben-Avraham, Journal of Statistical Physics

"Typically . . . students need broad exposure to a subject, as well as specific 'handles' to grasp. They need the step-by-step approach this book supplies. They need to experience the pleasure of unfolding a calculable model and of executing a computation that does what it is supposed to do. Many students, younger and older, will find the way Gould and Tobochnik's text satisfies these needs just about perfect."—Don S. Lemons, American Journal of Physics

"This is an ambitious book written by two experienced researchers and teachers. Starting from the microscopic dynamics of atoms and molecules, it uses statistical mechanical ideas to explain the thermodynamic behavior of macroscopic systems, and amply illustrates these ideas using hands-on computer simulations. Both teachers and students will find this book stimulating and rewarding."—Joel L. Lebowitz, Rutgers University

"This is an excellent book. It is better than any other textbook I have encountered for an undergraduate course in statistical thermodynamics. The authors' use of simulations to build a student's intuition is novel, and the problems and examples are very useful. They bring out the important issues and are a real asset in getting students to think about the subject."—William Klein, Boston University

"In addition to being a clear, comprehensive introduction to the field, this book includes a unique and welcome feature: an emphasis on computer simulations. These are integral to the exposition and provide key insights into fundamental concepts that so often confuse newcomers to the field. Simulations also give students a tool to investigate interesting topics that are normally considered too advanced for undergraduates. I highly recommend this book to anyone planning to teach undergraduate statistical and thermal physics."—Jon Machta, University of Massachusetts Amherst

"Gould and Tobochnik are respected researchers in the field and have a good sense of what is significant. Statistical and Thermal Physics includes many problems, exercises, and enlightening commentaries. The textbook places unique emphasis on numerical simulation techniques and what one can learn from them, and closely integrates them into the presentation. This is a welcome innovation."—Theodore L. Einstein, University of Maryland