PHYS 414


Statistical Mechanics, Spring 2019

                


Lecture Notes


1: Einstein's atomic proof, Brownian motion, Fokker-Planck equation

Slides: turtles all the way down
       Movie: Minimum energy path of the ATP hydrolysis reaction in the myosin II binding pocket, MPG [credits: Stefan Fischer research group]
       Movie: Molecular dynamics simulation of HIV capsid proteins, MPG [credits: Klaus Schulten research group]

2: Dynamical theories, laws of probability, applications of Bayes' theorem

3: Markovian approximation, master equation, stationary states, microscopic reversbility
     Slides: Example of a kinetic network and its trajectories
       Movie: Network trajectory, MP4
     Extra notes: Mastering the master equation

4: Uniqueness of stationary solution, Kullback-Leibler divergence

5: Microcanonical ensemble, ergodicity and mixing, time reversal symmetry, detailed balance

6: The big picture, entropy and the second law derived from properties of KL divergence

7: Entropy and information, Shannon source coding theorem

8: Additivity of entropy, the entropy of the universe (and its eventual heat death), temperature, free energy minimization

9: Entropy flow, heat, irreversible entropy production

10: Coupling the system to an external potential, work and free energy, Kelvin-Planck statement of the second law

11: Multiple heat baths, universal Carnot efficiency, engines vs. heat pumps

12: Equilibrium statistical mechanics as a limiting case: the zoo of potentials, Maxwell relations

13: Statistical mechanics in the trajectory picture: Gallavotti-Cohen, Crooks fluctuation theorems, Jarzynski equality

14: Quantum ensembles, density operators, von Neumann entropy, superoperators