33-765 Statistical Physics
Department of Physics, Carnegie Mellon University, Spring Term 2014, Deserno
1st problem sheet, due on Wednesday, January 22nd
1. Pairwise and mutual independence (3 points)
We ip a fair coin twice and see whether it falls head
33-765 Statistical Physics
Department of Physics, Carnegie Mellon University, Spring Term 2014, Deserno
4th problem sheet, due on Wednesday, February 12th
9. Another inequality just for good measure! (7 points)
a) Let p(x) and p0 (x) be two continuous pro
33-765 Statistical Physics
Department of Physics, Carnegie Mellon University, Spring Term 2014, Deserno
5th problem sheet, due on Wednesday, February 19th
12. Three very simple Legendre transforms (4 points)
The Legendre transform f (p) of a function f (x
33-765 Statistical Physics
Department of Physics, Carnegie Mellon University, Spring Term 2014, Deserno
7th problem sheet, due on Wednesday, March 19th
17. Adiabatic compression (4 points)
a) Show that, quite generally,
cP
T
=
=: ,
S
cV
(1)
1
where S = V
Microstate of the ideal gas in momentum space:
Equidistribution on energy surface and the partitioning between two compartments
Markus Deserno
Department of Physics, Carnegie Mellon University, Pittsburgh, PA 51213, USA
(Dated: January 22, 2013)
The equal
33-765 Statistical Physics
Department of Physics, Carnegie Mellon University, Spring Term 2014, Deserno
2nd problem sheet, due on Wednesday, January 29th
3. Statistical independence (5 points)
Consider a two-dimensional p-density PX,Y (x, y) for two rando
33-765 Statistical Physics
Department of Physics, Carnegie Mellon University, Spring Term 2014, Deserno
11th problem sheet, due on Wednesday, April 23rd
29. A microscopic model of rubber (10 points)
Rubber consists of a network of cross-linked polymers, w
The probability density of the sum of two uncorrelated random variables
is not necessarily the convolution of its two marginal densities
Markus Deserno
Department of Physics, Carnegie Mellon University, 5000 Forbes Ave, Pittsburgh, PA 15213
(Dated: Februa
33765 Statistical Physics, Spring 2014
Markus Deserno
Introductory remarks
1. This is the second time I teach 33765. The previous generation of graduate students
served as involuntary beta-testers. Youll be pleased to learn that you get the
33-765 Statistical Physics
Department of Physics, Carnegie Mellon University, Spring Term 2014, Deserno
6th problem sheet, due on Wednesday, February 26th
14. All reversible heat engines have the same efciency (8 points)
A reversible heat engine operating
33-765 Statistical Physics
Department of Physics, Carnegie Mellon University, Spring Term 2014, Deserno
12th problem sheet, due on Wednesday, April 30th
31. Equivalent characterizations of pure quantum states (4 points)
If we have a normalized state vecto