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Lecture Notes on Equilibrium Statistical Mechanics (Physics 211)
Course Information
Quick Summary of Statistical Mechanics
Probability, energy and entropy
Entropy and information
Classical statistical mechanics
Meaning of equilibrium
Equipartition
Gibbs entropy / Partition Function / Free energy
Trading conserved quantities between reservoir and system // External forces
Molecular Dynamics Simulation of Thermalization
Two standard examples for a system coupled to an external field
Spontaneous Reactions
Non-equilibrium fluctuation theorems
Chemical reactions
Statistical mechanics with interactions - Ising models
Finite dimensional Ising models
Variational Method
Interacting Gases
Monte Carlo, Markov Chains, and the Metropolis Algorithm
Debye-Hückel theory - charge screening
Brownian Motion as a Free Energy Minimizing Process
Coarse-graining and Ergodic Theory
When does quantum mechanics make a difference?
Gapless Quantum Matter: Phonons and the Debye Model, Goldstone’s Theorem
Formalism of quantum statistical mechanics
Hilbert space of Bosons and Fermions
Pressure of a dilute ideal quantum gase
Ideal quantum gases - Degenerate Fermi gas
Ideal quantum gases - Bose-Einstein Condensate
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