In statistical mechanics, the relation $\sigma^2_E=\langle E^2\rangle-\langle E\rangle^2=k_BT^2C_v$ is interpreted ad one of the examples of fluctuation-dissipation theorem. The fluctuation in energy is directly related to the ability of the system to absorb (or dissipate) energy.
In grand canonical ensemble, one finds that the number fluctuation is given by $$\sigma^2_N=\langle N^2\rangle-\langle N\rangle^2=\frac{\kappa_T}{\beta V}N^2.$$ Can this be regarded as an example of the fluctuation-dissipation theorem? If yes, which quantity on the RHS is the dissipative term? And why?