Introduction to Statistical Mechanics

Copyright © 2014-2015 by Peter Eastman

This work may be freely distributed under the terms of the Creative Commons Attribution-NoDerivatives 4.0 International License. The source can be found at https://github.com/peastman/statmech.

Contents

• 1. Introduction
• 2. The Statistical Description of Physical Systems
  • 2.1. Microstates and Macrostates
  • 2.2. The Density of States
  • 2.3. The Postulate of Equal a priori Probabilities
  • 2.4. Time Averages and Ensemble Averages
  • 2.5. The Maxwell-Boltzmann Distribution
  • 2.6. Thermodynamic Forces
  • 2.7. Probabilities of Macrostates
  • 2.8. Thermodynamic Potentials
  • 2.9. Averages
  • 2.10. Quantum Statistical Mechanics
• 3. Mathematical Interlude: Very Large Numbers
  • 3.1. The Binomial Distribution
  • 3.2. The Central Limit Theorem
• 4. The Interpretation of Statistical Quantities
  • 4.1. Temperature
  • 4.2. Thermodynamic Potentials as a Measure of Probability
  • 4.3. Independent and Dependent Variables
  • 4.4. Thermodynamic Potentials and Thermodynamic Forces
  • 4.5. The Mechanics of Thermodynamic Forces
  • 4.6. Thermal Equilibrium
  • 4.7. Intensive and Extensive Variables
  • 4.8. A Brief Rant: Internal Energy
• 5. Thermodynamics
  • 5.1. Thermodynamic Processes
  • 5.2. The Laws of Thermodynamics
  • 5.3. The Second Law of Thermodynamics
  • 5.4. Heat and Entropy
  • 5.5. Heat Capacity
  • 5.6. The Ideal Gas Law
  • 5.7. Heat Engines
  • 5.8. Free Energy
• 6. Phase Transitions
  • 6.1. A Qualitative Description of Phase Transitions
  • 6.2. Phase Diagrams
  • 6.3. Critical Points
  • 6.4. Metastable Phases and Ergodicity Breaking
  • 6.5. The Ising Model
  • 6.6. Non-Interacting Spins
  • 6.7. Mean Field Theory
• 7. Friction and Fluctuations
  • 7.1. Friction and Dissipation
  • 7.2. Linear Response Theory
  • 7.3. Fluctuations
  • 7.4. The Langevin Equation
  • 7.5. Diffusion of a Brownian Particle
  • 7.6. The Fluctuation-Dissipation Theorem
• 8. Evolution of Phase Space Probabilities
  • 8.1. Phase Space Probability Density
  • 8.2. Liouville’s Theorem
  • 8.3. The Approach to Equilibrium