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A Modern Course in Statistical Physics

A Modern Course in Statistical Physics is a textbook that illustrates the foundations of equilibrium and non-equilibrium statistical physics, and the universal nature of thermodynamic processes, from the point of view of contemporary research problems. The book treats such diverse topics as the microscopic theory of critical phenomena, superfluid dynamics, quantum conductance, light scattering, transport processes, and dissipative structures, all in the framework of the foundations of statistical physics and thermodynamics. It shows the quantum origins of problems in classical statistical physics. One focus of the book is fluctuations that occur due to the discrete nature of matter, a topic of growing importance for nanometer scale physics and biophysics. Another focus concerns classical and quantum phase transitions, in both monatomic and mixed particle systems. This fourth edition extends the range of topics considered to include, for example, entropic forces, electrochemical processes in biological systems and batteries, adsorption processes in biological systems, diamagnetism, the theory of Bose-Einstein condensation, memory effects in Brownian motion, the hydrodynamics of binary mixtures. A set of exercises and problems is to be found at the end of each chapter and, in addition, solutions to a subset of the problems is provided. The appendices cover Exact Differentials, Ergodicity, Number Representation, Scattering Theory, and also a short course on Probability.
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Table of Contents

Preface to the Fourth Edition XIII 1 Introduction 1 2 Complexity and Entropy 5 2.1 Introduction 5 2.2 Counting Microscopic States 5 2.3 Probability 9 2.4 Multiplicity and Entropy of Macroscopic Physical States 11 2.5 Multiplicity and Entropy of a Spin System 12 2.6 Entropic Tension in a Polymer 16 2.7 Multiplicity and Entropy of an Einstein Solid 18 2.8 Multiplicity and Entropy of an Ideal Gas 20 2.9 Problems 23 3 Thermodynamics 27 3.1 Introduction 27 3.2 Energy Conservation 29 3.3 Entropy 30 3.4 Fundamental Equation of Thermodynamics 35 3.5 Thermodynamic Potentials 38 3.6 Response Functions 46 3.7 Stability of the Equilibrium State 51 3.8 Cooling and Liquefaction of Gases 61 3.9 Osmotic Pressure in Dilute Solutions 64 3.10 The Thermodynamics of Chemical Reactions 67 3.11 The Thermodynamics of Electrolytes 74 3.12 Problems 78 4 The Thermodynamics of Phase Transitions 87 4.1 Introduction 87 4.2 Coexistence of Phases: Gibbs Phase Rule 88 4.3 Classification of Phase Transitions 89 4.4 Classical Pure PVT Systems 91 4.5 Binary Mixtures 105 4.6 The Helium Liquids 108 4.7 Superconductors 114 4.8 Ginzburg-Landau Theory 116 4.9 Critical Exponents 123 4.10 Problems 130 5 Equilibrium Statistical Mechanics I - Canonical Ensemble 135 5.1 Introduction 135 5.2 Probability Density Operator - Canonical Ensemble 137 5.3 Semiclassical Ideal Gas of Indistinguishable Particles 139 5.4 Interacting Classical Fluids 145 5.5 Heat Capacity of a Debye Solid 149 5.6 Order-Disorder Transitions on Spin Lattices 153 5.7 Scaling 162 5.8 Microscopic Calculation of Critical Exponents 169 5.9 Problems 177 6 Equilibrium Statistical Mechanics II - Grand Canonical Ensemble 183 6.1 Introduction 183 6.2 The Grand Canonical Ensemble 184 6.3 Adsorption Isotherms 187 6.4 Virial Expansion for Interacting Classical Fluids 191 6.5 Blackbody Radiation 197 6.6 Ideal Quantum Gases 200 6.7 Ideal Bose-Einstein Gas 202 6.8 Bogoliubov Mean Field Theory 210 6.9 Ideal Fermi-Dirac Gas 214 6.10 Magnetic Susceptibility of an Ideal Fermi Gas 220 6.11 Momentum Condensation in an Interacting Fermi Fluid 224 6.12 Problems 231 7 Brownian Motion and Fluctuation-Dissipation 235 7.1 Introduction 235 7.2 Brownian Motion 236 7.3 The Fokker-Planck Equation 240 7.4 Dynamic Equilibrium Fluctuations 250 7.5 Linear Response Theory and the Fluctuation-Dissipation Theorem 255 7.6 Microscopic Linear Response Theory 264 7.7 Thermal Noise in the Electron Current 272 7.8 Problems 273 8 Hydrodynamics 277 8.1 Introduction 277 8.2 Navier-Stokes Hydrodynamic Equations 278 8.3 Linearized Hydrodynamic Equations 289 8.4 Light Scattering 297 8.5 Friction on a Brownian particle 303 8.6 Brownian Motion with Memory 307 8.7 Hydrodynamics of Binary Mixtures 311 8.8 Thermoelectricity 318 8.9 Superfluid Hydrodynamics 322 8.10 Problems 329 9 Transport Coefficients 333 9.1 Introduction 333 9.2 Elementary Transport Theory 334 9.3 The Boltzmann Equation 341 9.4 Linearized Boltzmann Equations for Mixtures 343 9.5 Coefficient of Self-Diffusion 348 9.6 Coefficients of Viscosity and Thermal Conductivity 351 9.7 Computation of Transport Coefficients 359 9.8 Beyond the Boltzmann Equation 365 9.9 Problems 366 10 Nonequilibrium Phase Transitions 369 10.1 Introduction 369 10.2 Near Equilibrium Stability Criteria 370 10.3 The Chemically Reacting Systems 372 10.4 The Rayleigh-Benard Instability 378 10.5 Problems 385 Appendix A Probability and Stochastic Processes 387 A.1 Probability 387 A.2 Stochastic Processes 402 A.3 Problems 415 Appendix B Exact Differentials 417 Appendix C Ergodicity 421 Appendix D Number Representation 425 D.1 Symmetrized and Antisymmetrized States 425 D.2 The Number Representation 431 Appendix E Scattering Theory 437 E.1 Classical Dynamics of the Scattering Process 437 E.2 The Scattering Cross Section 440 E.3 Quantum Dynamics of Low-Energy Scattering 442 Appendix F Useful Math and Problem Solutions 445 F.1 Useful Mathematics 445 F.2 Solutions for Odd-Numbered Problems 447 References 453 Index 459

About the Author

Linda E. Reichl is Professor of Physics at the University of Texas at Austin and Co-Director of the Center for Complex Quantum Systems. Her research ranges over a number of topics in statistical physics and nonlinear dynamics. They include quantum transport theory, Brownian motion, quantum, classical and stochastic chaos theory, quantum control of atomic and cold atomic systems, and the conductance and spectral properties of open quantum systems. Professor Reichl has published more than 160 research papers, two books, A Modern Course in Statistical Physics and The Transition to Chaos, each of which have appeared in several editions. In 2000, she was elected Fellow of the American Physical Society "for her original contributions to the field of quantum chaos."


"This fourth edition extends the range of topics considered to include, for example, entropic forces, electrochemical processes in biological systems and batteries, adsorption processes in biological systems, diamagnetism, the theory of Bose-Einstein condensation, memory effects in Brownian motion, the hydronamics of binary mixtures." (Zentralblatt MATH 1334 2016)

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