Physics 210B
Time/Location:  M W 9:30 – 10:50am; MYRA 5623 
Lecturer:  Prof. Terry Hwa; Urey 7222 phone: 47263; email: 
grader:  TBA 
Office Hours:  Lecturer: After class or by appointment 
Course URL:  this page (https://matisse.ucsd.edu/courses/w24neqsm/) 
Grade  45 problem sets (to be posted below); inclass or takehome final. Scheduled final time: 811am, 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 Htheorem and the equilibrium distribution
 hydrodynamics
 Stochastic Markov processes
 random walk and diffusion
 Langevin dynamics; correlation and response functions
 the FokkerPlanck equation; stationary and timedependent 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 & RichterDyn 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; longrange interaction; Boltzmann’s Htheorem; equilibrium soln [note]  
L4  Mon, Jan 22  approach to equilibrium; conservation laws [note]  
L5  Wed, Jan 24  zerothorder and firstorder 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 FokkerPlanck 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  timedependent solution to the FokkerPlanck equation; biased random walk and intro to rare events [note]  
L13  Mon, Feb 26  rareevent statistics and the extremal ensemble [note]  HW3 soln 
L14  Wed, Feb 28  extremal statistics; birthdeath process; ztransform [note] [noteapp]  HW4 due Mon, Mar 11 
L15  Mon, Mar 4  stochastic dynamics of spatiallyextended 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; modecoupling approximation; exact distribution function in 1d [note]  HW5 due Wed Mar 20 