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