PHYS 414


Foundations of Statistical Mechanics, Spring 2025

                


Lecture Notes


(1) 1-13-25: Course overview; introduction to nonequilibrium thermodynamics: Video, Slides.

(2) 1-15-25: 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) 1-17-25: Trajectories and ensembles, the basics of probability theory, Bayes' rule: Video, Notes.

(4) 1-24-25: Understanding Bayes' rule: posterior, prior, and likelihood; fitting models to data: Video, Notes.

(5) 1-27-25: Application of Bayesian model fitting: dense neural networks: Video, Notes.

(6) 1-29-25: The Markovian assumption and its consequences: calculating the probabilities of trajectories and states: Video, Notes.

(7) 1-31-25: Transition probability graphs, continuous vs discrete descriptions of system states and time, existence of stationary probabilities: Video, Notes.

(8) 2-3-25: Classifying transition graphs (ergodicity and microscopic reversibility), mean hitting times, uniqueness of the stationary distribution for ergodic networks: Video, Notes.

(9) 2-5-25: Stationary states and algorithms: Google PageRank; setting up a framework for statistical physics: phase space in classical mechanics: Video, Notes.

(10) 2-7-25: Phase space, ergodicity, mixing; Fermi-Pasta-Ulam-Tsingou (FPUT) system: normal modes, canonical transformations: Video, Notes.

(11) 2-10-25: FPUT continued, nonlinear perturbations, integrable systems, action-angle coordinates: Video, Notes.

(12) 2-12-25: Physics on hypertori (donuts), KAM theorem (deformed donuts): Video, Notes.

(13) 2-14-25: KAM theorem continued, three body problem, from integrability to chaos in classical and quantum systems: Video, Notes.

(14) 2-17-25: Consequences of ergodicity and mixing; Feynman's ratchet and pawl; macrostates versus microstates: Video, Notes.

(15) 2-19-25: Time reversal symmetry, deriving the local detailed balance condition: Video, Notes.

(16) 2-21-25: Defining temperature, Boltzmann equilibrium: Video, Notes.

(17) 2-24-25: ``Gas of spins'' toy model: Video, Notes.

(18) 2-26-25: Returning to the trajectory picture: forward and reverse ensembles, irreversibility, the integral fluctuation theorem (IFT): Video, Notes.

(19) 2-28-25: Exploring the IFT, defining equilibrium and non-equilibrium stationary states: Video, Notes.

(20) 3-3-25: Work and entropy along a trajectory: Video, Notes.

(21) 3-5-25: Conservative versus non-conservative work, first and second laws for an isolated system: Video, Notes.

(22) 3-7-25: IFT unpacked: maximization of entropy for isolated systems, minimization of free energy for systems coupled to a thermal environment: Video, Notes.

(23) 3-21-25: Interpreting entropy as information: the Shannon source coding theorem: Video, Notes.

(24) 3-24-25: Changing environments, cyclically driven systems, Kelvin-Planck statement of the second law, Jarzynski equality: Video, Notes.

(25) 3-26-25: Experimental validation of Jarzynski equality, multiple temperature environments: Video, Notes.

(26) 3-28-25: Thermodynamic laws for multiple temperatures, Carnot efficiency bound, the uselessness of maximum efficiency: Video, Notes.

(27) 3-31-25: Thermodynamic bounds on heat pumps / refrigerators, the many ``children'' of the IFT, linear thermodynamics: Video, Notes.