Solution
= Solution
Substitution of the canonical probabilities into the <Gibbs entropy> gives
$$
S=-k_B\sum_np_n(-\beta E_n-\log Z)
=k_B\log Z+k_B\beta E.
$$
Hence
$$
\boxed{S=k_B\log Z+\frac ET}.
$$
= Solution
Substitution of the canonical probabilities into the <Gibbs entropy> gives
$$
S=-k_B\sum_np_n(-\beta E_n-\log Z)
=k_B\log Z+k_B\beta E.
$$
Hence
$$
\boxed{S=k_B\log Z+\frac ET}.
$$