distributions. We thus return to the pion gas example from section \[GCECE\] and restrict the discussion to simple momentum space cuts in rapidity, transverse momentum, and azimuthal angle, see also the Appendix for details.

Results {#Results}
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Multiplicity fluctuations in the full momentum space
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Let us firstly recall basic properties of multiplicity fluctuations of negative particles in the full momentum space ($4\pi$ fluctuations) in the three standard ensembles, of the Boltzmann pion gas considered here.

Multiplicity fluctuations in the CE are suppressed due to exact charge conservation. For a neutral ($Q=0$) system one finds in the large volume limit $\omega_{4\pi}^{ce} = 0.5$ [@CEfluc1]. Further suppression of fluctuations arise from additionally enforcing exact energy conservation in the MCE. Here one finds $\omega_{4\pi}^{mce} \approx 0.25$ for a Boltzmann pion gas at $T\approx 160MeV$. In the GCE, since no conservation laws are enforced, we always find a Poisson distribution with width $\omega_{4\pi}^{gce} =1$.

Since charge conservation in CE links the distributions of negatively charged particles to the one of their positive counterparts, i.e. $P(N_-) = P(N_+-Q)$, the relative width of $P(N_-)$ increases (decreases) as we move the electric charge density to positive (negative) values [@CEfluc2]. This can be easily be seen from 