Define a quantity \(J\) as

\[
J=E-N \mu=T S-P V
\]

Show that for a system in the grand canonical ensemble

\[
\overline{(\Delta J)^{2}}=k T^{2} C_{V}+\left\{\left(\frac{\partial U}{\partial N}ight)_{T, V}-\muight\}^{2} \overline{(\Delta N)^{2}}
\]