Show that the entropy of a system in the grand canonical ensemble can be written as [

Question:

Show that the entropy of a system in the grand canonical ensemble can be written as
\[
S=-k \sum_{r, s} P_{r, s} \ln P_{r, s}
\]
where \(P_{r, s}\) is given by equation (4.1.9).


Equation (4.1.9)

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