PHYS 414


Statistical Mechanics, Spring 2018

                


Syllabus

  • 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