PHYS 414


Statistical Mechanics, Spring 2021

                


Syllabus

  • Stochastic processes: review of probability concepts, Bayes theorem, Bayesian model estimation
  • Markovian approximation, master equation, stationary states, microscopic reversbility
  • Continuous time master equation, Kullback-Leibler divergence, uniqueness of stationary solution, f-divergences
  • Adjoint master equation, survival probability, mean first passage times
  • Microcanonical ensemble, ergodicity and mixing, time reversal symmetry, detailed balance
  • Entropy and the second law derived from properties of KL divergence
  • Additivity of entropy, the entropy of the universe (and its eventual heat death), temperature, free energy minimization
  • Entropy flow, heat, irreversible entropy production
  • Coupling a system to external degrees of freedom: entropy flow and work
  • Kelvin-Planck statement of second law of thermodynamics
  • Systems coupled to multiple heat baths, universal Carnot efficiency bound
  • Optimality in heat engines and heat pumps, the tradeoff between efficiency and power output
  • Properties of equilibrium systems, Maxwell's relations
  • The trajectory formalism in statistical physics, defining entropy production along a trajectory
  • Fluctuation theorems: Gallavotti-Cohen, Crooks, and integral versions
  • Quantum statistical mechanics: ensembles and density operators
  • Decompositions of the density operator, von Neumann entropy, time evolution in isolated quantum systems
  • Distinction between von Neumann and classical thermodynamic entropy, how the density operator changes under measurement
  • Measurements as special case of open quantum systems, Choi-Kraus representation theorem
  • Quantum master equation, Lindblad operators, decoherence