Galperin Spring 2004
Contents
1 General Comments 5
2 Introduction to Thermodynamics 7
2.1 Additional Problems: Fluctuations . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.2 Mini-tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.2.1 A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.2.2 B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3 The Thermodynamics of Phase Transitions 33
3.1 Mini-tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.1.1 A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.1.2 B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4 Elementary Probability Theory . . . 49
5 Stochastic dynamics ... 59
6 The Foundations of Statistical Mechanics 77
7 Equilibrium Statistical Mechanics 79
8 Tests and training 103
A Additional information 107
A.1 Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
A.1.1 Thermodynamic potentials . . . . . . . . . . . . . . . . . . . . . . . . . 107
A.1.2 Variable transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
A.1.3 Derivatives from the equation of state . . . . . . . . . . . . . . . . . . . 107
A.2 Main distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
A.3 The Dirac delta-function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
A.4 Fourier Series and Transforms . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
B Maple Printouts 115
3
4 CONTENTS
Chapter 1
General Comments
This year the course will be delivered along the lines of the book [1]. The problems will also be
selected from this book. It is crucially important for students to solve problems independently.
The problems will be placed on the course homepage. The same page will contain solutions
of the problems. So if a student is not able to solve the problem without assistance, then she/he
should come through the solution. In any case, student have to able to present solutions, obtained
independently, or with help of the course homepage.
FYS 3130 (former FYS 203) is a complicated course, which requires basic knowledge of
classical and quantum mechanics, electrodynamics, as
