Equilibrium thermodynamics describes average quantities, but microscopic systems continually fluctuate around those averages. Statistical mechanics relates the size of equilibrium fluctuations to macroscopic response functions.

In the canonical ensemble, $$\langle E\rangle=-\frac{\partial\ln Z}{\partial\beta}.$$ Differentiating again gives $$\operatorname{Var}(E)=\langle E^2\rangle-\langle E\rangle^2 =\frac{\partial^2\ln Z}{\partial\beta^2}.$$ Using $\beta=1/(k_BT)$ and $$C_V=\left(\frac{\partial\langle E\rangle}{\partial T}\right)_V,$$ one obtains $$\operatorname{Var}(E)=k_BT^2C_V.$$ Thus a system with larger heat capacity exhibits larger absolute energy fluctuations at the same temperature.

For an extensive system, both $\langle E\rangle$ and $C_V$ typically scale with particle number $N$. The standard deviation therefore scales as $\sqrt N$ while the mean scales as $N$, so relative fluctuations behave roughly as $$\frac{\sigma_E}{\langle E\rangle}\sim\frac{1}{\sqrt N}.$$ This explains why macroscopic thermodynamic variables appear effectively deterministic despite microscopic fluctuations.

Similar fluctuation-response relations connect particle-number fluctuations to compressibility and magnetization fluctuations to magnetic susceptibility. The broader lesson is that response and noise are two sides of equilibrium statistical behavior: how strongly a system fluctuates encodes how strongly it responds to an applied thermodynamic field.