Statistical Mechanics · Problem 4.13

Formulation of Quantum Statistics — R. K. Pathria

Physics — Statistical Mechanics · grand-canonical-energy-fluctuation-J

Problem

Define a quantity JJ as J=E−Nμ=TS−PV.J = E - N\mu = TS - PV. Show that for a system in the grand canonical ensemble (ΔJ)2‾=kT2CV+{(∂U∂N)T,V−μ}2(ΔN)2‾.\overline{(\Delta J)^2} = kT^2 C_V + \left\{\left(\frac{\partial U}{\partial N}\right)_{T,V} - \mu\right\}^2 \overline{(\Delta N)^2}.

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