PHYS 414

Statistical Mechanics, Spring 2020


Online virtual blackboard notes

4-29-20: Quantum master equation, Lindblad operators, decoherence of a spin-1/2 particle, open questions: PDF, Video.

4-27-20: Derivation of Choi-Kraus representation theorem, continued: PDF, Video.

4-24-20: Measurements as special case of open quantum systems, Choi-Kraus representation theorem: PDF, Video.

4-22-20: Distinction between von Neumann and classical thermodynamic entropy, how the density operator changes under measurement: PDF, Video.

4-20-20: Decompositions of the density operator, von Neumann entropy, time evolution in isolated quantum systems: PDF, Video.

4-17-20: Ensembles and density operators: PDF, Video.

4-15-20: Testing the IFT part III, introduction to quantum statististical mecahanics: PDF, Video.

4-13-20: Testing the IFT part II: experimentally measuring internal entropy production: PDF, Video.

4-10-20: Integral fluctuation theorem (IFT) implies the second law, testing the theorem in an AFM force spectroscopy experiment: PDF, Video.

4-8-20: Fluctuation theorems: Gallavotti-Cohen, Crooks, and integral versions: PDF, Video.

4-6-20: Setting up the trajectory formalism in statistical physics, defining entropy production along a trajectory: PDF, Video.

4-3-20: The zoo of thermodynamic potentials and Maxwell's relations derived from a single dynamical equation: PDF, Video.

4-1-20: Properties of equilibrium systems, combining the first and second laws into a single description of system dynamics: PDF, Video.

3-30-20: Optimality in heat engines and heat pumps, the tradeoff between efficiency and power output: PDF, Video.

3-27-20: Systems coupled to multiple heat baths, universal Carnot efficiency bound: PDF, Video.

3-25-20: Kelvin-Planck statement of second law of thermodynamics: PDF, Video.

3-23-20: Coupling a system to external degrees of freedom: entropy flow and work: PDF, Video.

3-20-20: Generalizing the entropy decomposition, in the spirit of Prigogine; definition of equilibrium (it's boring): PDF, Video.

3-18-20: Breaking down entropy into system and environmental components, irreversible entropy production: PDF, Video.

Lecture Notes

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: Network trajectory, MP4
     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