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PHY 418: Statistical Mechanics I
Prof. S. Teitel: stte@pas.rochester.edu ---- Spring 2025

Notes

Notes 0 - Review of probability and the Thermodynamic Limit of large numbers
Unit 1 - Classical Thermodynamics
- Notes 1-1 - Postulates and Variables of Classical Thermodynamics
- Notes 1-2 - Conditions for Equilibrium, Concavity of the Entropy
- Notes 1-3 - The Gibbs-Duhem Relation, Entropy of the Ideal Gas, Energy Minimum Principle
- Notes 1-4 - Legendre Transformations
- Notes 1-5 - Free Energies
- Notes 1-6 - Reservoirs and the Extremum Principles for Free Energy
- Notes 1-7 - The Maxwell Relations
- Notes 1-8 - Response Functions
- Notes 1-9 - Stability and Response Functions
- Notes 1-10 - Heat Engines
- Notes 1-10-supp - Supplemental note on the Carnot Cycle
- Notes 1-10-supp2 - Supplemental note: Adiabatic, Reversible, Quasistatic, etc., and Some Examples
Unit 2 - Classical Ensembles
- Notes 2-1 - Kinetic Theory of the Ideal Gas and the Maxwell Velocity Distribution
- Notes 2-2 - The Ergodic Hypothesis -- Time vs Ensemble Averages
  
  A review of ergodic theory may be found here.
- Notes 2-3 - Liouville's Theorem
- Notes 2-4 - The Microcannonical Ensemble and Entropy
- Notes 2-5 - Entropy of the Ideal Gas in the Microcanonical Ensemble
- Notes 2-6 - Entropy of Mixing and the Gibbs Paradox
- Notes 2-7 - Indistinguishable Particles
- Notes 2-8 - The Canonical Ensemble
- Notes 2-9 - Equivalence of the Microcanonical and Canonical Ensembles
- Notes 2-10 - Average Energy Vs Most Probably Energy; Stirling's Formula
- Notes 2-11 - Factorization of the Canonical Partition Function for Non-Interacting Particles
- Notes 2-12 - The Virial Theorem and the Equipartition Theorem for Classical Systems
- Notes 2-13 - Examples: The Specific Heat of Solids, Curie Paramagnetism
- Notes 2-14 - A Note About the Proper Choice of Coordinates
- Notes 2-15 - Entropy and Information
- Notes 2-16 - The Grand Canonical Ensemble
- Notes 2-17 - The Grand Canonical Ensemble and the Grand Potential
- Notes 2-18 - Non-Interacting Particles in the Grand Canonical Ensemble
- Notes 2-19 - Chemical Equilibrium and an Example: A Gas in Equillibrium with Adsorption Sites
Unit 3 - Quantum Ensembles
- Notes 3-1 - Quantum Ensembles and the Density Matrix
  
  Two recent papers on the relation between quantum ensembles and thermodynamics
  Eigenstate Thermalization in a Locally Perturbed Integrable System
  Entanglement and the foundations of statistical mechanics
- Notes 3-2 - Quantum Many Particle Systems -- Bosons vs Fermions
- Notes 3-3 - Particle in a Box States, the Two Particle Density Matrix
- Notes 3-4 - Quantum Partition Function for Non-Interacting Particles
- Notes 3-5 - Average Occupation Numbers and Comparison of Quantum and Classical Ideal Gases
- Notes 3-6 - The Quantized Harmonic Oscillator as Bosons, the Debye Model for the Specific Heat of a Solid
- Notes 3-7 - Black Body Radiation
- Notes 3-8 - The Quantum Ideal Gas and the Leading Quantum Correction to the Ideal Gas Law
- Notes 3-9 - The Degenerate Fermi Gas, the Sommerfeld Model for Electrons in a Conductor
- Notes 3-10 - Pauli Paramagnetism of the Electron Gas
- Notes 3-11 - The Ideal Bose Gas and Bose-Einstein Condensation
- Notes 3-Supplement - The Chemical Potential: Classical vs Quantum, Non-Relativistic vs Relativistic, Particle vs Oscillator
Unit 4 - Phase Transitions
- Notes 4-1 - Classical Spin Models
- Notes 4-2 - The Ising Model -- A Qualitative Discussion
- Notes 4-3 - The Mean-Field Approxximation for the Ising Model
- Notes 4-4 - Critical Exponents within the Mean-Field Approximation
- Notes 4-5 - The Maxwell Construction and the Gibbs Free Energy
- Notes 4-6 - The Liquid-Gas Phase Transition
- Notes 4-7 - The Infinite Range Ising Model and the 1D Ising Model
- Notes 4-8 - Fluctuations and the Ginzburg Criterion