PHYSICS 210B : NONEQUILIBRIUM STATISTICAL PHYSICS
HW SOLUTIONS #1 : PROBABILITY
(1) A six-sided die is loaded in such a way that it is twice as likely to yield an even number
than an odd number when thrown.
(a) Find the distribution cfw_pn consistent wit
Lecture Notes on Nonequilibrium Statistical Physics
(A Work in Progress)
Daniel Arovas
Department of Physics
University of California, San Diego
November 18, 2014
Contents
1
Fundamentals of Probability
1
1.1
References . . . . . . . . . . . . . . . . . .
PHYSICS 210B : NONEQUILIBRIUM STATISTICAL PHYSICS
HW ASSIGNMENT #5 : APPLICATIONS
(1) Consider the gamblers ruin problem in which two players A and B gamble repeatedly
against each other by betting $1 on each trial. The probability of A winning in any giv
PHYSICS 210B : NONEQUILIBRIUM STATISTICAL PHYSICS
HW SOLUTIONS #5 : APPLICATIONS
(1) Consider the gamblers ruin problem in which two players A and B gamble repeatedly
against each other by betting $1 on each trial. The probability of A winning in any give
PHYSICS 210B : NONEQUILIBRIUM STATISTICAL PHYSICS
HW ASSIGNMENT #4 : DIFFUSION
(1) A diffusing particle is conned to the interval [0, L]. The diffusion constant is D and
the drift velocity is vD . The boundary at x = 0 is absorbing and that at x = L is re
PHYSICS 210B : NONEQUILIBRIUM STATISTICAL PHYSICS
HW SOLUTION #4 : DIFFUSION
(1) A diffusing particle is conned to the interval [0, L]. The diffusion constant is D and
the drift velocity is vD . The boundary at x = 0 is absorbing and that at x = L is reec
PHYSICS 210B : NONEQUILIBRIUM STATISTICAL PHYSICS
HW ASSIGNMENT #3 : STOCHASTIC CALCULUS
(1) Evaluate, for general , the averages of the following stochastic integrals:
t
dW (s) W (s) s
0
t
t
3
s
dW (s) W (s) e
,
dW (s) W 2k+1 (s) .
,
0
0
(2) Derive Eqn.
PHYSICS 210B : NONEQUILIBRIUM STATISTICAL PHYSICS
HW SOLUTIONS #3 : STOCHASTIC CALCULUS
(1) Evaluate, for general , the averages of the following stochastic integrals:
t
t
dW (s) W (s) s
t
3
,
s
dW (s) W (s) e
0
dW (s) W 2k+1 (s) .
,
0
0
Solution:
We eval
PHYSICS 210B : NONEQUILIBRIUM STATISTICAL PHYSICS
HW ASSIGNMENT #2 : STOCHASTIC PROCESSES
(1) Show that for time scales sufciently greater than 1 that the solution x(t) to the
Langevin equation x + x = (t) describes a Markov process. You will have to cons
PHYSICS 210B : NONEQUILIBRIUM STATISTICAL PHYSICS
HW SOLUTIONS #2 : STOCHASTIC PROCESSES
(1) Show that for time scales sufciently greater than 1 that the solution x(t) to the
Langevin equation x + x = (t) describes a Markov process. You will have to const
PHYSICS 210B : NONEQUILIBRIUM STATISTICAL PHYSICS
HW ASSIGNMENT #1 : PROBABILITY
(0) Study the eight worked example problems linked on the HOMEWORK web page.
(1) A six-sided die is loaded in such a way that it is twice as likely to yield an even number
th