Winter 2024: Non-equilibrium Statistical Mechanics

Physics 210B 

Time/Location: M W 9:30 – 10:50am; MYR-A 5623
Lecturer: Prof. Terry Hwa; Urey 7222
phone: 4-7263; e-mail: 
grader: TBA
Office Hours: Lecturer: After class or by appointment
Course URL: this page (https://matisse.ucsd.edu/courses/w24-neq-sm/)
Grade 4-5 problem sets (to be posted below); in-class or take-home final.
Scheduled final time: 8-11am, Wednesday Mar 20, 2024
Prerequisite: PHYS 210A (equilibrium stat mech); or equivalent.

Course outline

  • Approach to equilibrium
    • phase space and Liouville’s theorem
    • kinetic theory; the BBGKY hierarchy
    • Boltzmann’s H-theorem and the equilibrium distribution
    • hydrodynamics
  • Stochastic Markov processes
    • random walk and diffusion
    • Langevin dynamics; correlation and response functions
    • the Fokker-Planck equation; stationary and time-dependent solns
    • multiplicative noise: Ito vs Stratanovich dynamics
  • Applications
    • escape over barrier
    • flux through random potential
    • biased random walk and extremal statistics
    • random energy model; glassy dynamics; “aging”
    • absorbing boundaries; evolution and population genetics
  • Interacting systems
    • stochastic field theory: symmetries and conservation law
    • dynamic scaling: driven diffusion and kinetic roughening
    • asymmetric exclusion processes

Reference Books:

No book is required for this course. The book by Kerson Huang would be a good reference for the first topic (Approach to Equilibrium). The book by van Kampen on stochastic processes is always a good reference to have if you work on stochastic processes. You may also want to consult a book by Goel & Richter-Dyn on stochastic problems in biology.

Course activity:

  Date Topics assignment
L1 Mon, Jan 8 Intro: phase space, density unction, Liouville’s theorem; equilibration [note] HW1 due
Mon Jan 29
L2 Wed, Jan 10 kinetic theory: BBGKY hierarchy; collision integral; derivation of Boltzmann equation [note]
  Mon, Jan 15 Martin Luther King, Jr Day  
L3 Wed, Jan 17 molecular chaos and the Boltzmann eqn; long-range interaction; Boltzmann’s H-theorem; equilibrium soln [note]  
L4 Mon, Jan 22 approach to equilibrium; conservation laws [note]
L5 Wed, Jan 24 zeroth-order and first-order hydrodynamics [note]
L6 Mon, Jan 29 Intro to stochastic dynamics: random walk, Brownian motion [note]
L7 Wed, Jan 31 Langevin dynamics; simple response and correlation function [note]
HW2 due
Wed, Feb 14
L8 Mon, Feb 5 Derivations of the Fokker-Planck equation [note] HW1 soln 
L9 Wed, Feb 7 multiplicative noise; Ito vs Stratanovich dynamics [note]  
L10 Mon, Feb 12 equilibrium and nonequilibrium steady states; hopping over kinetic barrier [note]  
L11 Wed, Feb 14 driven transport in random potential [note (updated Feb 21)]  HW3 due Mon Feb 26 (updated Feb 21)
  Mon, Feb 19 President’s Day HW2 soln 
L12 Wed, Feb 21 time-dependent solution to the Fokker-Planck equation; biased random walk and intro to rare events [note]  
L13 Mon, Feb 26 rare-event statistics and the extremal ensemble [note] HW3 soln 
L14 Wed, Feb 28 extremal statistics; birth-death process; z-transform [note] [note-app] HW4 due
Mon, Mar 11
L15 Mon, Mar 4 stochastic dynamics of spatially-extended systems;
1d Ising model: Glauber vs Kawasaki dynamics [note]
 
L16 Wed, Mar 6 linear stochastic dynamics; correlation function [note]  
L17 Mon, Mar 11 dynamic scaling function; conservative dynamics; generalized Einstein relation; intro to KPZ equation [note]
L18 Wed, Mar 13 perturbative solution to KPZ eqn; mode-coupling approximation; exact distribution function in 1d [note] HW5 due
Wed Mar 20