all other variables are set to their peak values, e.g. $Q=V\kappa_1^Q$, $E=V\kappa_1^E$, $\vec P = \vec 0$. The second and more practical way is to use an approximation similar to Eq.(\[MCE\_MultNormal\]) to describe the macro state $Q^j = (Q,E,\vec P)$. The normalization in Eq.(\[MCEprob2\]), $\mathcal{Z}^{E,Q,\vec P}$, is then given by the 5-dimensional integral, similar to Eq.(\[MCEInt\]), without the integration over $\phi_{N_{\Omega}}$. The 1-dimensional slice along $N_{\Omega}$, i.e. the conditional distribution of particle number $N_{\Omega}$, while charge, energy and momentum are fixed to $Q,E,\vec P = \vec 0$, can then be shown [@clt] to converge to a Gaussian in the large volume limit: $$\begin{aligned}
\label{PMCE}
P_{mce}(N_{\Omega} ) ~ \simeq~  \frac{1}{\left(2\pi ~\omega^{mce}_{\Omega}
   ~ \langle N_{\Omega} \rangle   \right)^{1/2}} ~  \exp  \left(- \frac{ \left(
      N_{\Omega} - \langle N_{\Omega} \rangle \right)^2}{2
    ~  \omega^{mce}_{\Omega} ~ \langle  N_{\Omega} \rangle  } \right) ~. \end{aligned}$$ The scaled variance $\omega^{mce}_{\Omega}$ is given by the ratio of the two determinants of the two relevant second rank cumulants, $\kappa_2$ and $\tilde
\kappa_2$, of the two partition functions $\mathcal{Z}^{N_{\Omega},E,Q,\vec
  P}$ and $\mathcal{Z}^{E,Q,\vec P}$, hence[^2]: $$\label{SimpleOmega}
\omega^{mce}_{\Omega} =  \frac{ \det | \kappa_2| }{
  \kappa_1^{N_{\Omega}} \;\det| \tilde \kappa_2|  }~.$$ The asymptotic ($V\rightarrow \infty$) scaled variance can therefore be written in the form of Eq.(28) in 