(b) A certain system can occupy one of N states. The expression Pi is the probability for the system to occupy state i (i = 1, . . . ,N). Show with the help of the result of

(a) that the maximum entropy is given by S = k ln N. (5.65)

Note the difference between cases

(a) and (b). The result (5.65) is that for the maximized entropy

(different from (5.62)). Compare also with Eq. (5.11).

[Hint: Use the method of Lagrangian multipliers to link δS, δPi].