## PHYS 414## Statistical Mechanics, Spring 2020 |

1: Overview of the course

2: Coarse-graining a physical system: turtles all the way down

3: Stochastic processes: review of probability concepts, Bayes theorem, Bayesian model estimation

4: Markovian approximation, master equation, stationary states, microscopic reversbility

Slides: Example of a kinetic network and its trajectories

Movie:

Extra notes: Mastering the master equation

5: Continuous time master equation, Kullback-Leibler divergence, uniqueness of stationary solution, f-divergences

6: Adjoint master equation, survival probability, mean first passage time, example: Poisson distribution and disease spreading

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

Three-body simulator to explore KAM and chaotic regimes

8: Simple "spin gas" example illustrating ergodicity, mixing, and detailed balance

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

10: Entropy and information, Shannon source coding theorem

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

12: Temperature in the spin gas toy model, entropy flow, heat, irreversible entropy production