  Multiplicity fluctuations in limited segments of momentum space are
calculated for a classical pion gas within the statistical model. Results for
the grand canonical, canonical, and micro-canonical ensemble are obtained,
compared and discussed. We demonstrate that even in the large volume limit
correlations between macroscopic subsystems due to energy and momentum
conservation persist. Based on the micro-canonical formulation we make
qualitative predictions for the rapidity and transverse momentum dependence of
multiplicity fluctuations. The resulting effects are of similar magnitude as
the predicted enhancement due to a phase transition from a quark-gluon plasma
to a hadron gas phase, or due to the critical point of strongly interacting
matter, and qualitatively agree with recently published preliminary
multiplicity fluctuation data of the NA49 SPS experiment.
