We consider again the system in Exercises 1 and 2 and make use of the same notation.
We will study the limits T → 0 and T →∞.

(a) In the limit T → 0 compute the four probabilities given by Eq. (6.7) and compute
directly the entropy in Eq. (6.11) in this limit.

Equation (6.11)

Equation (6.7)

(b) In the limit T →∞compute the four probabilities given by Eq. (6.7) and compute
directly the entropy in Eq. (6.11) in this limit.

Equation (6.11)

Equation (6.7)

(c) Now use the expression valid for all temperatures in Eq. (6.121) and from this
expression derive the limting values of (a) and (b).

Equation (6.121)

S[p]=-Pilnpi i=1