## Statistical Mechanics

James Binney,
Michaelmas Term 2002
The course introduces statistical mechanics at the level required for the
Part A Theory Option. Option 6 in Part B assumes knowledge of this
material. The course introduces the principle of maximum
entropy as a general law of deductive reasoning and treats statistical
mechanics as a series of applications of this general principle.

Two problem sets will be issued

### 1 What's it all about?

### 2 The principle of maximum entropy

### 3 The canonical distribution

- 3.0.1 ln Z as a generating function
- 3.0.2 Linear response theorem
- 3.0.3 Composite systems

- 3.1 Spin-half paramagnet
- 3.2 Ideal Gases
- 3.2.1 Case of a specified number of particles
- 3.2.2 Bose--Einstein condensation
- 3.2.3 Degenerate matter

### 4 The Grand Canonical Distribution

- 4.1 Application to a perfect gas
- 4.2 Application to an e+/- plasma

### 5 The Microcanonical distribution

- 5.1 Dynamics of a rubber band
- 5.2 Fluctuations
- 5.3 General remarks

### 6 Strongly interacting systems

- 6.1 Models
- 6.1.1 The Ising model
- 6.1.2 The lattice gas
- 6.1.3 $\beta$-brass

- 6.2 Evaluating Z(Ising)

### 7 Mean-field theory

- 7.1 Mean-field theory of the non-ideal gas