PHYS 414


Statistical Mechanics, Spring 2024

                


Lecture Notes


(1) 1-17-24: Course overview; introduction to nonequilibrium thermodynamics: Video, Slides.

(2) 1-19-24: 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) 1-22-24: Trajectories and ensembles, the basics of probability theory, Bayes' rule: Video, Notes.

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

(5) 1-26-24: Application of Bayesian model fitting: dense neural networks: Video, Notes.

(6) 1-29-24: The Markovian assumption and its consequences: calculating the probabilities of trajectories and states: Video, Notes.

(7) 1-31-24: Transition probability graphs, continuous vs discrete descriptions of system states and time, stationary probabilities: Video, Notes.

(8) 2-2-24: Existence of stationary distributions, classifying transition graphs (ergodicity and microscopic reversibility), mean hitting times: Video, Notes.

(9) 2-5-24: Calculating mean hitting times, uniqueness of stationary distribution for ergodic networks, Google PageRank: Video, Notes.

(10) 2-7-24: Setting up a physical framework for statistical mechanics: phase space, ergodicity, mixing: Video, Notes.

(11) 2-9-24: Fermi-Pasta-Ulam-Tsingou system: normal modes, canonical transformations, nonlinear perturbations: Video, Notes.

(12) 2-12-24: Integrable systems, action-angle coordinates, physics on hypertori, KAM theorem, "deformed donuts": Video, Notes.

(13) 2-14-24: From integrability to chaos in classical and quantum systems; the consequences of ergodicity and mixing; Feynman's ratchet and pawl: Video, Notes.

(14) 2-16-24: Macrostates versus microstates, time reversal symmetry, deriving the local detailed balance condition: Video, Notes.

(15) 2-19-24: Counting microstates, defining temperature: Video, Notes.

(16) 2-21-24: Boltzmann equilibrium, "gas" of spins toy model: Video, Notes.

(17) 2-23-24: Spin toy model continued: positive and negative absolute temperatures: Video, Notes.

(18) 2-26-24: Returning to the trajectory picture: forward and reverse ensembles, irreversibility, the integral fluctuation theorem (IFT): Video, Notes.

(19) 2-28-24: Conequences of the IFT, system coupling to external work, deriving the second law of thermodynamics: Video, Notes.

(20) 3-1-24: Conservative versus non-conservative work, first and second laws for an isolated system: Video, Notes.
          Note: because of a problem with the recording, the video for this lecture is an older version covering the same material.

(21) 3-4-24: IFT unpacked: maximization of entropy for isolated systems, minimization of free energy for systems coupled to a thermal environment: Video, Notes.

(22) 3-6-24: Interpreting entropy as information: the Shannon source coding theorem: Video, Notes.

(23) 3-8-24: Source coding theorem continued, equilibrium vs. nonequilibrium stationary states: Video, Notes.

(24) 3-18-24: Changing environments, cyclically driven systems and the Kelvin-Planck statement of the second law: Video, Notes.
          Note: because of an audio problem with the recording, the video for this lecture is an older version covering the same material.

(25) 3-20-24: Jarzynski equality: Video, Notes.

(26) 3-22-24: Multiple temperature environments, Carnot efficiency bound: Video, Notes.

(27) 3-27-24: Maximal efficiency is useless, thermodynamic bounds on heat pumps / refrigerators, the many ``children'' of the IFT: Video, Notes.

(28) 3-29-24: Linear thermodynamics, forces and fluxes, Onsager coefficients, electrical circuit examples: Video, Notes.

(29) 4-1-24: General properties of the Onsager coefficient matrix, Onsager reciprocity, fluctuation-dissipation theorem: Video, Notes.

(30) 4-3-24: Fluctuation-dissipation theorem examples: diffusion of a Brownian particle, Johnson-Nyquist noise, Seebeck and Peltier effects: Video, Notes.

(31) 4-5-24: Properties of equilibrium, the zoo of thermodynamic potentials and minimization principles: Video, Notes.

(32) 4-10-24: Equilibrium phase transitions and renormalization, part I: the Ising model, calculating physical observables from the partition function: Video, Notes.

(33) 4-12-24: Equilibrium phase transitions and renormalization, part II: first and second order phase transitions, critical exponents, universality: Video, Notes.

(34) 4-15-24: Equilibrium phase transitions and renormalization, part III: RG as coarse-graining, exact RG on fractal lattices: Video, Notes.

(35) 4-17-24: Equilibrium phase transitions and renormalization, part IV: Exact RG calculation, flows and fixed points: Video, Notes.

(36) 4-19-24: Equilibrium phase transitions and renormalization, part V: Deriving scaling exponents from RG, universality; Quantum statistical mechanics: ensembles and density operators: Video, Notes.

(37) 4-22-24: Decompositions of density operators, defining von Neumann entropy, time evolution of closed quantum systems and the non-increase of von Neumann entropy: Video, Notes.

(38) 4-24-24: Open quantum systems, measurements, the Choi-Kraus representation theorem: Video, Notes.

(39) 4-26-24: Quantum master equations for closed and open systems, jump and dephasing operators, two-state example: Video, Notes.