Lecture Notes from PHYS603 - Methods of Statistical Mechanics, as taught by Dr. Paulo Bedaque in the Spring, 2016 semester.

Lecture 1 (02/02/16): Foundations of Statistical Mechanics
- Tricks to Doing Statistical Mechanics
- Classical Systems & Phase Space
- Ergodic Hypothesis & Ergodic Systems
- Computing Observables
- Introducing Thermodynamics

Lecture 2 (02/04/16): Fundamentals of Entropy
- Ensembles & Macro/microstates
- The Archetypical Thermodynamics Problem
- Potential Energy -> # of microstates -> Entropy
- Liouville's Theorem and the Incompressibility of Hamiltonian Flow
- The Case of Mixing Systems (Ergodic Systems)

Lecture 3 (02/09/16): Thermodynamics
- Relevant Properties of Entropy
- Solving for E(S,V,N)
- Equations of State
- Non-relativistic, Monoatomic, Non-interacting Gas Example

Lecture 4 (02/11/16): Energy & Entropy from Equations of State
- Quantum Statistical Correction to our Entropy Equation
- Equations of State for a Free Gas
- Euler Relation
- Recovering Energy & Entropy

Lecture 5 (02/18/16): Efficiency of Machines
- The Carnot Cycle
- Quasi-Static Approximation
- Stability

Lecture 6 (02/23/16): Stability
- Stability
- Isothermal Compressibility
- The Canonical Ensemble

Lecture 7 (02/25/16): Legendre Transform of Ensembles 
- Canonical Ensembles
- The Thermodynamical Limit
- Legendre Transforms
- Helmholtz Free Energy

Lecture 8 (03/01/16): Free Energy
- Helmholtz Free Energy
- Ideal Gas Example
- Solid with Magnetic Dipoles example
- Independent Harmonic Oscillators example

Lecture 9 (03/03/16): Quantum Statistical Mechanics
- Independent Harmonic Oscillators example
- Quantum Statistical Mechanics
- Density Matrices
- Quantum Harmonic Oscillators example