PHYS 414

Statistical Mechanics, Spring 2022


Lecture Notes

(1) 1-10-22: Course overview; introduction to nonequilibrium thermodynamics (part 1/2): Video, Slides.

(2) 1-12-21: Overview of nonequilibrium thermodynamics (part 2/2): Video, Slides.
                    Coarse-graining physical systems (micro- vs. macro-states, seven ways of looking at a protein, turtles all the way down): Slides.

(3) 1-14-22: Basics of stochastic processes: trajectories and ensembles.
                    Review of probability concepts: joint, marginal, and conditional probabilities; Bayes theorem: Video, Notes.

(4) 1-19-22: Bayes theorem example continued; the Bayesian interpretation of fitting a theoretical model to data: Video, Notes.

(5) 1-21-22: Machine learning as Bayesian fitting (part 1/2): Video, Notes.

(6) 1-24-22: Machine learning as Bayesian fitting (part 2/2); Markovian assumption for coarse-grained system dynamics: Video, Notes.

(7) 1-26-22: Consequences of the Markovian assumption; transition matrices and the time evolution of state probabilities: Video (1/2), Video (2/2), Notes.

(8) 1-28-22: Master equation example, taxonomy of dynamical equations, stationary distributions: Video, Notes.

(9) 1-31-22: Existence of a stationary distribution; classification of network graphs; ergodicity, microscopic reversibility: Video, Notes.

(10) 2-2-22: Mean hitting times; uniqueness of stationary distribution for an ergodic network: Video, Notes.

(11) 2-7-22: Hitting times and Google Page Rank; connecting transition matrices to physics: classical dynamics in phase space: Video, Notes.

(12) 2-9-22: Ergodicity and mixing, microcanonical ensemble, Fermi-Pasta-Ulam-Tsingou numerical experiment: Video, Notes.

(13) 2-11-22: KAM theorem, three-body problem, ergodic billiards, Feynman's ratchet and pawl, system/environment distinction: Video, Notes.
                  Three-body simulator to explore KAM and chaotic regimes.

(14) 2-14-22: Connecting classical mechanics to the Markovian transition matrix; the stationary state distribution and time-reversal symmetry: Video, Notes.

(15) 2-16-22: Implications of local detailed balance; physical quantities conserved between the system and environment: Video, Notes.

(16) 2-18-22: Temperature and the Boltzmann distribution; the meaning of negative absolute temperature: Video, Notes.

(17) 2-21-22: Interacting spin gas example: ergodicity, local detailed balance, positive and negative absolute temperatures: Video, Notes.

(18) 2-23-22: Return to the trajectory picture; the definition of irreversibility: Video, Notes.

(19) 2-25-22: Integral fluctuation theorem: Video, Notes.

(20) 2-28-22: Physical consequences of the integral fluctuation theorem: work, heat, entropy and the first two laws of thermodynamics: Video, Notes.

(21) 3-2-22: Different faces of the second law: maximizing entropy, minimizing free energy: Video, Notes.

(22) 3-4-22: Interpreting entropy as information: the Shannon source coding theorem: Video, Notes.

(23) 3-14-22: Nonequilibrium stationary states; systems with time-dependent control parameters; Kelvin-Planck statement of the second law: Video, Notes.

(24) 3-16-22: Jarzynski equality and its experimental verification; system connected to multiple heat baths: Video, Notes.

(25) 3-18-22: System coupled to two thermal environments; deriving the Carnot efficiency bound: Video, Notes.

(26) 3-21-22: Refrigerator / heat pump performance bound; linear thermodynamics and Onsager coefficients: Video, Notes.

(27) 3-23-22: Onsager matrix of transport coefficients; the integral fluctuation theorem in the linear thermodynamic regime: Video, Notes.

(28) 3-25-22: Deriving Onsager reciprocity and the fluctuation-dissipation theorem; Einstein relation and Johnson-Nyquist noise: Video, Notes.

(29) 3-28-22: Efficiency of a heat engine at maximum power; Seebeck and Peltier effects in thermoelectric materials: Video, Notes.

(30) 3-30-22: Properties of equilibrium states: the zoo of chemical potentials: Video, Notes.

(31) 4-1-22: Maxwell relations, equipartition theorem, ideal gases: Video, Notes.

(32) 4-4-22: Ideal gas relations; efficiency of the Otto cycle for internal combustion engines: Video, Notes.

(33) 4-6-22: Electrical motor efficiency; introduction to quantum statistical mechanics: ensembles, observables, density operator: Video, Notes.

(34) 4-8-22: Properties of density operators; decompositions and von Neumann entropy: Video, Notes.

(35) 4-11-22: von Neumann versus thermodynamic entropy: differences for isolated systems under unitary time evolution: Video, Notes.

(36) 4-13-22: Evolution of density operators under measurement; Choi-Kraus representation theorem: Video, Notes.

(37) 4-18-22: Proof of the Choi-Kraus theorem: Video, Notes.

(38) 4-20-22: Lindblad equation (quantum master equation): Video, Notes.

(39) 4-22-22: Lindblad example: decoherence of a qubit; T1 and T2 times; emergence of the classical master equation: Video, Notes.

(40) 4-25-22: Connecting classical and quantum chaos: Berry-Tabor and BGS conjectures: Video, Notes.