The entropy of a system is given by S=−kB∑jfjlnfj, where fj is the probability of a microstate of the system. Each microstate of the fermion pre-gas model is described by specifying the occupation of all six orbital states.
a) Show that there are 26=64 possible microstates of the model system, and that there are therefore 64 terms in the expression for the entropy.
b) Show that this expression reduces to
S=−kBn,m∑fnmlnfnm
and that this equation contains only six terms. What special properties of the model effect this drastic reduction?