Suggestions for Further Reading

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Emery Spencer
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1 Contents Preface viii 1 From Microscopic to Macroscopic Behavior Introduction Some Qualitative Observations Doing Work and the Quality of Energy Some Simple Simulations Measuring the Pressure and Temperature Work, Heating, and the First Law of Thermodynamics *The Fundamental Need for a Statistical Approach *Time and Ensemble Averages Models of Matter The ideal gas Interparticle potentials Lattice models Importance of Simulations Dimensionless Quantities Summary Supplementary Notes Approach to equilibrium Mathematics refresher Vocabulary Additional Problems Suggestions for Further Reading i

2 ii 2 Thermodynamic Concepts Introduction The System Thermodynamic Equilibrium Temperature Pressure Equation of State Some Thermodynamic Processes Work The First Law of Thermodynamics Energy Equation of State Heat Capacities and Enthalpy Quasistatic Adiabatic Processes The Second Law of Thermodynamics The Thermodynamic Temperature The Second Law and Heat Engines Entropy Changes Equivalence of Thermodynamic and Ideal Gas Scale Temperatures The Thermodynamic Pressure The Fundamental Thermodynamic Relation The Entropy of an Ideal Classical Gas The Third Law of Thermodynamics Free Energies Thermodynamic Derivatives *Applications to Irreversible Processes Joule or free expansion process Joule-Thomson process Supplementary Notes The mathematics of thermodynamics Thermodynamic potentials and Legendre transforms Vocabulary Additional Problems Suggestions for Further Reading

3 iii 3 Concepts of Probability Probability in Everyday Life The Rules of Probability Mean Values The Meaning of Probability Information and uncertainty *Bayesian inference Bernoulli Processes and the Binomial Distribution Continuous Probability Distributions The Central Limit Theorem (or Why Thermodynamics Is Possible) *The Poisson Distribution or Should You Fly? *Traffic Flow and the Exponential Distribution *Are All Probability Distributions Gaussian? *Supplementary Notes Method of undetermined multipliers Derivation of the central limit theorem Vocabulary Additional Problems Suggestions for Further Reading Statistical Mechanics Introduction A Simple Example of a Thermal Interaction Counting Microstates Noninteracting spins A particle in a one-dimensional box One-dimensional harmonic oscillator One particle in a two-dimensional box One particle in a three-dimensional box Two noninteracting identical particles and the semiclassical limit The Number of States of Many Noninteracting Particles: Semiclassical Limit The Microcanonical Ensemble (Fixed E, V, andn) The Canonical Ensemble (Fixed T, V,andN) Connection Between Thermodynamics and Statistical Mechanics in the Canonical Ensemble Simple Applications of the Canonical Ensemble An Ideal Thermometer Simulation of the Microcanonical Ensemble

4 iv 4.11 Simulation of the Canonical Ensemble Grand Canonical Ensemble (Fixed T, V, and µ) *Entropy is not a Measure of Disorder Supplementary Notes The volume of a hypersphere Fluctuations in the canonical ensemble Vocabulary Additional Problems Suggestions for Further Reading Magnetic Systems Paramagnetism Noninteracting Magnetic Moments Thermodynamics of Magnetism The Ising Model The Ising Chain Exact enumeration Spin-spin correlation function Simulations of the Ising chain *Transfer matrix Absence of a phase transition in one dimension The Two-Dimensional Ising Model Onsager solution Computer simulation of the two-dimensional Ising model Mean-Field Theory *Phase diagram of the Ising model *Simulation of the Density of States *Lattice Gas Supplementary Notes The Heisenberg model of magnetism Low temperature expansion High temperature expansion *Bethe approximation Fully connected Ising model Metastability and nucleation Vocabulary Additional Problems

5 v Suggestions for Further Reading Many-Particle Systems The Ideal Gas in the Semiclassical Limit Classical Statistical Mechanics The equipartition theorem The Maxwell velocity distribution The Maxwell speed distribution Occupation Numbers and Bose and Fermi Statistics Distribution Functions of Ideal Bose and Fermi Gases Single Particle Density of States Photons Nonrelativistic particles The Equation of State of an Ideal Classical Gas: Application of the Grand Canonical Ensemble Blackbody Radiation The Ideal Fermi Gas Ground state properties Low temperature properties The Heat Capacity of a Crystalline Solid The Einstein model Debye theory The Ideal Bose Gas and Bose Condensation Supplementary Notes Fluctuations in the number of particles Low temperature expansion of an ideal Fermi gas Vocabulary Additional Problems Suggestions for Further Reading The Chemical Potential and Phase Equilibria Meaning of the chemical potential Measuring the chemical potential in simulations The Widom insertion method The chemical demon algorithm Phase Equilibria Equilibrium conditions Simple phase diagrams

6 vi Clausius-Clapeyron equation The van der Waals Equation of State Maxwell construction *The van der Waals critical point *Chemical Reactions Vocabulary Additional Problems Suggestions for Further Reading Classical Gases and Liquids Introduction Density Expansion The Second Virial Coefficient *Diagrammatic Expansions Cumulants High temperature expansion Density expansion Higher order virial coefficients for hard spheres The Radial Distribution Function Perturbation Theory of Liquids The van der Waals equation *The Ornstein-Zernike Equation and Integral Equations for g(r) *One-Component Plasma Supplementary Notes The third virial coefficient for hard spheres Definition of g(r) in terms of the local particle density X-ray scattering and the static structure function Vocabulary Additional Problems Suggestions for Further Reading Critical Phenomena Landau Theory of Phase Transitions Universality and Scaling Relations A Geometrical Phase Transition Renormalization Group Method for Percolation The Renormalization Group Method and the One-Dimensional Ising Model

7 vii 9.6 The Renormalization Group Method and the Two-Dimensional Ising Model Vocabulary Additional Problems Suggestions for Further Reading A.1 Physical Constants and Conversion Factors A.2 Hyperbolic Functions A.3 Approximations A.4 Euler-Maclaurin Formula A.5 Gaussian Integrals A.6 Stirling s Approximation A.7 Bernoulli Numbers A.8 Probability Distributions A.9 Fourier Transforms A.10 The Delta Function A.11 Convolution Integrals A.12 Fermi and Bose Integrals

INDEX 481. Joule-Thomson process, 86, 433. Kosterlitz-Thouless transition, 467

INDEX 481. Joule-Thomson process, 86, 433. Kosterlitz-Thouless transition, 467 Index accessible microstates, 173 183, 185, 196, 200, 201 additive random process, 146 adiabatic demagnetization, 235 expansion, 52, 61 process, 43 quasistatic, 49, 50 wall, 34 anharmonic oscillator, 349