  Particle number fluctuations are studied in the microcanonical ensemble. For
the Boltzmann statistics we deduce exact analytical formulae for the
microcanonical partition functions in the case of non-interacting massless
neutral particles and charged particles with zero net charge. The particle
number fluctuations are calculated and we find that in the microcanonical
ensemble they are suppressed in comparison to the fluctuations in the canonical
and grand canonical ensembles. This remains valid in the thermodynamic limit
too, so that the well-known equivalence of all statistical ensembles refers to
average quantities, but does not apply to fluctuations. In the thermodynamic
limit we are able to calculate the particle number fluctuations in the system
of massive bosons and fermions when the exact conservation laws of both the
energy and charge are taken into account.
