  It is shown that large chemical potential leads to the significant increase
of multiplicity fluctuations for bosons, and makes the fluctuations infinite in
the case of Bose-Einstein condensation. It allows to distinguish between the
models that explain the anomalous proton to pion ratio and the low transverse
momentum enhancement of pion spectra in Pb+Pb collisions at the LHC within
chemical equilibrium or non-equilibrium models. The effects of resonance
decays, finite size of the system, requirements to the event statistics,
different momentum cuts, and limited detector acceptance are considered. The
obtained results show the possibility to observe a substantial increase of the
normalized kurtosis for positively or negatively charged pions in the case of
non-equilibrium or partial pion condensation using currently measured data.
