Question: 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}
Define a quantity \(J\) as
\[
J=E-N \mu=T S-P V
\]
Show that for a system in the grand canonical ensemble
\[
\overline{(\Delta J)^{2}}=k T^{2} C_{V}+\left\{\left(\frac{\partial U}{\partial N}ight)_{T, V}-\muight\}^{2} \overline{(\Delta N)^{2}}
\]
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