PHYS 414


Foundations of Statistical Mechanics, Spring 2026

                


Lecture Notes


(1) 1-12-26: Course overview; introduction to nonequilibrium thermodynamics: Video, Slides.

(2) 1-14-26: Course overview continued, coarse-graining: Video.
                    Coarse-graining physical systems (micro- vs. macro-states, seven ways of looking at a protein, turtles all the way down): Slides.

(3) 1-16-26: Trajectories and ensembles, the basics of probability theory, Bayes' rule: Video, Notes.

(4) 1-21-26: Understanding Bayes' rule: posterior, prior, and likelihood; fitting models to data: Video, Notes.

(5) 1-23-26: Application of Bayesian model fitting: dense neural networks: Video, Notes.

(6) 1-28-26: The Markovian assumption and its consequences: calculating the probabilities of trajectories and states, master equation: Video, Notes.

(7) 1-30-26: Simulating trajectories, continuous vs discrete descriptions of system states and time, existence of stationary probabilities: Video, Notes.

(8) 2-2-26: Classifying transition graphs (ergodicity and microscopic reversibility), mean hitting times, uniqueness of the stationary distribution for ergodic networks: Video, Notes.

(9) 2-4-26: Stationary states and algorithms: Google PageRank; setting up a framework for statistical physics: phase space in classical mechanics: Video, Notes.

(10) 2-6-26: Phase space, ergodicity, mixing; Fermi-Pasta-Ulam-Tsingou (FPUT) system: normal modes, canonical transformations: Video, Notes.

(11) 2-9-26: FPUT continued, nonlinear perturbations, integrable systems, action-angle coordinates: Video, Notes.

(12) 2-11-26: Physics on hypertori (donuts), KAM theorem (deformed donuts), three body problem: Video, Notes.

(13) 2-13-26: From integrability to chaos in classical and quantum systems, consequences of ergodicity and mixing, Feynman's ratchet and pawl: Video, Notes.

(14) 2-16-26: Macrostates versus microstates, time reversal symmetry: Video, Notes.

(15) 2-18-26: Time reversal symmetry continued, deriving the local detailed balance condition: Video, Notes.

(16) 2-20-26: Consequences of local detailed balance, defining temperature: Video, Notes.

(17) 2-23-26: Interpreting temperature, Boltzmann equilibrium: Video, Notes.

(18) 2-25-26: ``Gas of spins'' toy model: Video, Notes.

(19) 2-27-26: Gas of spins continued, returning to the trajectory picture: forward and reverse ensembles, irreversibility: Video, Notes.

(20) 3-2-26: Integral fluctuation theorem, defining equilibrium and non-equilibrium stationary states: Video, Notes.

(21) 3-4-26: Coupling system to external work: Video, Notes.

(22) 3-6-26: Irreversibility decomposed into physical terms, conservative versus non-conservative work, first and second laws of thermodynamics: Video, Notes.