  We investigate event-by-event fluctuations for ensembles with non-fixed
multiplicity. Moments of event observable distributions, like total energy
distribution, total transverse momentum distribution, etc, are shown to be
related to the multi-body correlations present in the system. For classical
systems, these moments reduce in the absence of any correlations to the moments
of particle inclusive momentum distribution. As a consequence, a zero value for
the recently introduced $\Phi$-variable is shown to indicate the vanishing of
two-body correlations from one part, and of correlations between multiplicity
and momentum distributions from the other part. It is often misunderstood as a
measure of the degree of equilibration in the system.
