Thermodynamics and Statistical Mechanics

by Daniel Arovas

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Publisher
UC San Diego
Subjects
Physics, Thermodynamics and Statistical Mechanics
Licence
CC BY-NC-SA, as LibreTexts states it. Non-commercial use only.
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Tweens profiles and older, judged from its title and subjects

Contents

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  1. Front Matter
  2. TitlePage
  3. InfoPage
  4. Table of Contents
  5. Licensing
  6. 1: Fundamentals of Probability
  7. 1.1: Statistical Properties of Random Walks
  8. 1.2: Basic Concepts in Probability Theory
  9. 1.3: Entropy and Probability
  10. 1.4: General Aspects of Probability Distributions
  11. 1.5: Bayesian Statistical Inference
  12. 1.S: Summary
  13. 2: Thermodynamics
  14. 2.1: What is Thermodynamics?
  15. 2.2: The Zeroth Law of Thermodynamics
  16. 2.3: Mathematical Interlude - Exact and Inexact Differentials
  17. 2.4: The First Law of Thermodynamics
  18. 2.5: Heat Engines and the Second Law of Thermodynamics
  19. 2.6: The Entropy
  20. 2.7: Thermodynamic Potentials
  21. 2.8: Maxwell Relations
  22. 2.9: Equilibrium and Stability
  23. 2.10: Applications of Thermodynamics
  24. 2.11: Phase Transitions and Phase Equilibria
  25. 2.12: Entropy of Mixing and the Gibbs Paradox
  26. 2.13: Some Concepts in Thermochemistry
  27. 2.14: Appendix I- Integrating Factors
  28. 2.15: Appendix II- Legendre Transformations
  29. 2.16: Appendix III- Useful Mathematical Relations
  30. 2.S: Summary
  31. 3: Ergodicity and the Approach to Equilibrium
  32. 3.1: Modeling the Approach to Equilibrium
  33. 3.2: Phase Flows in Classical Mechanics
  34. 3.3: Irreversibility and Poincaré Recurrence
  35. 3.4: Remarks on Ergodic Theory
  36. 3.5: Thermalization of Quantum Systems
  37. 3.6: Appendices
  38. 3.S: Summary
  39. 4: Statistical Ensembles
  40. 4.1: Microcanonical Ensemble (μCE)
  41. 4.2: The Quantum Mechanical Trace
  42. 4.3: Thermal Equilibrium
  43. 4.4: Ordinary Canonical Ensemble (OCE)
  44. 4.5: Grand Canonical Ensemble (GCE)
  45. 4.6: Statistical Ensembles from Maximum Entropy
  46. 4.7: Ideal Gas Statistical Mechanics
  47. 4.8: Selected Examples
  48. 4.9: Statistical Mechanics of Molecular Gases
  49. 4.10: Appendix I- Additional Examples
  50. 4.S: Summary
  51. 5: Noninteracting Quantum Systems
  52. 5.1: Statistical Mechanics of Noninteracting Quantum Systems
  53. 5.2: Quantum Ideal Gases - Low Density Expansions
  54. 5.3: Entropy and Counting States
  55. 5.4: Lattice Vibrations - Einstein and Debye Models
  56. 5.5: Photon Statistics
  57. 5.6: The Ideal Bose Gas
  58. 5.7: The Ideal Fermi Gas
  59. 5.8: The Ideal Fermi Gas
  60. 5.9: Appendix I- Second Quantization
  61. 5.10: Appendix II- Ideal Bose Gas Condensation
  62. 5.11: Appendix III- Example Bose Condensation Problem
  63. 5.S: Summary
  64. 6: Classical Interacting Systems
  65. 6.1: Ising Model
  66. 6.2: Nonideal Classical Gases
  67. 6.3: Lee-Yang Theory
  68. 6.4: Liquid State Physics
  69. 6.5: Coulomb Systems - Plasmas and the Electron Gas
  70. 6.6: Polymers
  71. 6.7: Appendix I- Potts Model in One Dimension
  72. 6.S: Summary
  73. 7: Mean Field Theory of Phase Transitions
  74. 7.1: The van der Waals system
  75. 7.2: Fluids, Magnets, and the Ising Model
  76. 7.3: Mean Field Theory
  77. 7.4: Variational Density Matrix Method
  78. 7.5: Landau Theory of Phase Transitions
  79. 7.6: Mean Field Theory of Fluctuations
  80. 7.7: Global Symmetries
  81. 7.8: Ginzburg-Landau Theory
  82. 7.9: Appendix I- Equivalence of the Mean Field Descriptions
  83. 7.10: Appendix II- Additional Examples
  84. 7.S: Summary
  85. 8: Nonequilibrium Phenomena
  86. 8.1: Equilibrium, Nonequilibrium and Local Equilibrium
  87. 8.2: Boltzmann Transport Theory
  88. 8.3: Weakly Inhomogeneous Gas
  89. 8.4: Relaxation Time Approximation
  90. 8.5: Diffusion and the Lorentz model
  91. 8.6: Linearized Boltzmann Equation
  92. 8.7: The Equations of Hydrodynamics
  93. 8.8: Nonequilibrium Quantum Transport
  94. 8.9: Stochastic Processes
  95. 8.10: Appendix I- Boltzmann Equation and Collisional Invariants
  96. 8.11: Appendix II- Distributions and Functionals
  97. 8.12: Appendix III- General Linear Autonomous Inhomogeneous ODEs
  98. 8.13: Appendix IV- Correlations in the Langevin formalism
  99. 8.14: Appendix V- Kramers-Krönig Relations
  100. 8.S: Summary
  101. 9: Renormalization
  102. 9.1: The Program of Renormalization
  103. 9.2: Real Space Renormalization
  104. 9.3: Block Spin Transformation
  105. 9.4: Scaling Variables
  106. 9.5: RSRG on Hierarchical Lattices The
  107. 9.S: Summary
  108. Back Matter
  109. Index
  110. Index
  111. Glossary
  112. Detailed Licensing