## PHYS 414## Statistical Mechanics, Spring 2019 |

- Einstein's atomic proof: random walks, Brownian motion, diffusion
- Coarse-graining physical theories, laws of probability, Bayes' theorem and its applications
- Markovian approximation, master equation, ergodicity, and the approach to equilibrium
- Time reversibility and detailed balance
- Ergodicity in the microcanonical ensemble
*f*-divergences and the second law of thermodynamics- Entropy, free energies, and manipulating convex functions: the nature of equilibrium
- Generalizing the second law: Crooks fluctuation theorem and the Jarzynski equality
- Nonequilibrium experiments and free energy reconstruction
- Stochastic dynamics: Kramers-Moyal expansion and the Fokker-Planck equation
- Langevin equation, fluctuation-dissipation theorem, and the Green-Kubo relations
- First-passage times, escape over a barrier, and the Arrhenius law
- Quantum statistical mechanics: density matrices and the quantum Liouville equation
- Bose and Fermi gases
- Quantum master equation and qubit decoherence
- Coarse-graining and the renormalization group
- Ising model, phase transitions, and scaling near the critical point