$P_{ce}(N_{\Omega})$, i.e. the multiplicity distribution of $\pi^-$ with momenta inside $\Omega$, while $\omega_{4\pi}$ is the width of the corresponding distribution when $\Omega$ is extended to the full momentum space. It can immediately be seen that this formula is consistent with acceptance scaling, Eq.(\[accscaling\]), $\omega_{\Omega} ~=~ 1 + q \left(\omega_{4\pi} -1 \right)$, if $q \equiv
z^-_{\Omega}/z$. Generally we find $\omega^{ce}_{4\pi} < \omega^{ce}_{\Omega}
< \omega^{gce}=1$. In the limit of $z^-_{\Omega}/z \rightarrow 0$ we approach the Poisson limit of a ‘random‘ distribution with $\omega = 1$, i.e. the observed part of the system is embedded into a much larger charge bath and the GCE is a valid description.

Micro-Canonical Ensemble {#MCE}
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For the MCE an analytical solution seems to be out of reach presently, so we use instead the asymptotic solution, applicable to large systems, derived in [@clt]. In order to avoid unnecessary repetition of calculations, we will only give a general outline here, and refer the reader for a detailed discussion to Ref.[@clt]. It should be mentioned that this method be would be also applicable to systems of finite spatial extention, provided the average particle number in a given momentum space bin exceeds roughly $\langle N_{\Omega}\rangle \gtrsim 5$. In this work 