P_{gce} \left(N_{\Omega} \right) ~\equiv~ Z^{-1}_{gce} \times \int
\limits_{-\pi}^{\pi} \frac{d\phi_{N_{\Omega}}}{2\pi} ~ e^{-iN_{\Omega}
  \phi_{N_{\Omega}} } ~ \mathcal{Z} \left( \phi_{N_{\Omega}}\right) ~=~
\frac{\left(z^-_{\Omega}\right)^{N_{\Omega}}}{N_{\Omega}!} 
\exp \left[- z^-_{\Omega} \right]~,\end{aligned}$$ where the system partition function is given by $ Z_{gce} \equiv \mathcal{Z}
\left( \phi_{N_{\Omega}} = 0\right) $, and $z^-_{\Omega} =
z^-_{\Omega} \left(\phi_{N_{\Omega}}=0 \right)$. Independent of the shape or size of $\Omega$ we find a Poissonian for the multiplicity distribution Eq.(\[GCEPDF\]). Thus, using Eq.(\[ScaledVar\]), one finds for the scaled variance $\omega^{gce}_{\Omega} = 1$, since $\langle
N_{\Omega} \rangle = z^-_{\Omega}$, and $\langle N^2_{\Omega}
\rangle = \langle N_{\Omega} \rangle^2 + \langle N_{\Omega} \rangle$.

For Bose and Fermi statistics one does not expect a Poisson distribution and (in particular when the chemical potential is large) deviations from a Poissonian can be large. Thus one expects also deviations from Eq.(\[accscaling\]) when considering only finite acceptance.

Canonical Ensemble
------------------

In the CE the heat bath is still assumed to be infinite, while we remove the charge bath and drop the chemical potential. Thus, we introduce a further Wick-rotated fugacity $\mu/T \rightarrow  i \phi_Q $ into the single particle partition functions to account for global (however not in the momentum space segment $\Omega$) conservation of electric charge $Q$. Particles in $\Omega$ are therefore correlated, 