Statistical Physics

Summing Up: Recommended. Upper-division undergraduates. (Choice, 1 March 2014) The best choice is finally that the entropy is uncertainty commodified". The reviewer believes that the aim of the book is evident and it is worthwhile to make a detailed study of it from time to time. (Zentralblatt MATH, 1 October 2013)

Ian Ford Department of Physics and Astronomy, University College London, UK

Preface xiii 1. Disorder or Uncertainty? 1 2. Classical Thermodynamics 5 2.1 The Classical Laws of Thermodynamics 5 2.2 Macroscopic State Variables and Thermodynamic Processes 6 2.3 Properties of the Ideal Classical Gas 8 2.4 Thermodynamic Processing of the Ideal Gas 10 2.5 Entropy of the Ideal Gas 13 2.6 Entropy Change in Free Expansion of an Ideal Gas 15 2.7 Entropy Change due to Nonquasistatic Heat Transfer 17 2.8 Cyclic Thermodynamic Processes, the Clausius Inequality and Carnots Theorem 19 2.9 Generality of the Clausius Expression for Entropy Change 21 2.10 Entropy Change due to Nonquasistatic Work 23 2.11 Fundamental Relation of Thermodynamics 25 2.12 Entropy Change due to Nonquasistatic Particle Transfer 28 2.13 Entropy Change due to Nonquasistatic Volume Exchange 30 2.14 General Thermodynamic Driving 31 2.15 Reversible and Irreversible Processes 32 2.16 Statements of the Second Law 33 2.17 Classical Thermodynamics: the Salient Points 35 Exercises 35 3. Applications of Classical Thermodynamics 37 3.1 Fluid Flow and Throttling Processes 37 3.2 Thermodynamic Potentials and Availability 39 3.2.1 Helmholtz Free Energy 40 3.2.2 Why Free Energy? 43 3.2.3 Contrast between Equilibria 43 3.2.4 Gibbs Free Energy 44 3.2.5 Grand Potential 46 3.3 Maxwell Relations 47 3.4 Nonideal Classical Gas 48 3.5 Relationship between Heat Capacities 49 3.6 General Expression for an Adiabat 50 3.7 Determination of Entropy from a Heat Capacity 50 3.8 Determination of Entropy from an Equation of State 51 3.9 Phase Transitions and Phase Diagrams 52 3.9.1 Conditions for Coexistence 53 3.9.2 ClausiusClapeyron Equation 55 3.9.3 The Maxwell Equal Areas Construction 57 3.9.4 Metastability and Nucleation 59 3.10 Work Processes without Volume Change 59 3.11 Consequences of the Third Law 60 3.12 Limitations of Classical Thermodynamics 61 Exercises 62 4. Core Ideas of Statistical Thermodynamics 65 4.1 The Nature of Probability 65 4.2 Dynamics of Complex Systems 68 4.2.1 The Principle of Equal a Priori Probabilities 68 4.2.2 Microstate Enumeration 71 4.3 Microstates and Macrostates 72 4.4 Boltzmanns Principle and the Second Law 75 4.5 Statistical Ensembles 77 4.6 Statistical Thermodynamics: the Salient Points 78 Exercises 79 5. Statistical Thermodynamics of a System of Harmonic Oscillators 81 5.1 Microstate Enumeration 81 5.2 Microcanonical Ensemble 83 5.3 Canonical Ensemble 84 5.4 The Thermodynamic Limit 88 5.5 Temperature and the Zeroth Law of Thermodynamics 91 5.6 Generalisation 91 Exercises 92 6. The Boltzmann Factor and the Canonical Partition Function 95 6.1 Simple Applications of the Boltzmann Factor 95 6.1.1 MaxwellBoltzmann Distribution 95 6.1.2 Single Classical Oscillator and the Equipartition Theorem 97 6.1.3 Isothermal Atmosphere Model 98 6.1.4 Escape Problems and Reaction Rates 99 6.2 Mathematical Properties of the Canonical Partition Function 99 6.3 Two-Level Paramagnet 101 6.4 Single Quantum Oscillator 103 6.5 Heat Capacity of a Diatomic Molecular Gas 104 6.6 Einstein Model of the Heat Capacity of Solids 105 6.7 Vacancies in Crystals 106 Exercises 108 7. The Grand Canonical Ensemble and Grand Partition Function 111 7.1 System of Harmonic Oscillators 111 7.2 Grand Canonical Ensemble for a General System 115 7.3 Vacancies in Crystals Revisited 116 Exercises 117 8. Statistical Models of Entropy 119 8.1 Boltzmann Entropy 119 8.1.1 The Second Law of Thermodynamics 120 8.1.2 The Maximum Entropy Macrostate of Oscillator Spikiness 122 8.1.3 The Maximum Entropy Macrostate of Oscillator Populations 122 8.1.4 The Third Law of Thermodynamics 126 8.2 Gibbs Entropy 127 8.2.1 Fundamental Relation of Thermodynamics and Thermodynamic Work 129 8.2.2 Relationship to Boltzmann Entropy 130 8.2.3 Third Law Revisited 131 8.3 Shannon Entropy 131 8.4 Fine and Coarse Grained Entr