Overview: Statistical mechanics
Aims
- You should be able to write down an expression for the information contained in a non-uniform distribution.
- You should be able to state the principle of equal apriori probabilities.
- You should be able to use Lagrange's method of undetermined multipliers to derive the expressions for the generalized partition function. In particular, you should be able to derive expression for the probability of being in a microstate, an expression for the generalised partition function and expressions that relate ensemble averages of extensive quantities to partial derivatives of the partition function.
- You should be able to derive the key expressions for the canonical distribution. In particular, you should be able to derive an expression for the probability of being in a microstate, an expression for the canonical partition function and expressions that relate the ensemble average of the energy and the heat capacity to first and second derivatives of the partition function respectively.