Pion Number Fluctuations and Correlations in the Statistical System with Fixed Isospin

The statistical system of pions with zero total isospin is studied. The suppression effects for the average yields due to isospin conservation are the same for $\pi^0$, $\pi^+$ and $\pi^-$. However, a behavior of the corresponding particle number fluctuations are different. For neutral pions there is the enhancement of the fluctuations, whereas for charged pions the isospin conservation suppresses fluctuations. The correlations between the numbers of charged and neutral pions are observed for finite systems. This causes a maximum of the total pion number fluctuations for small systems. The thermodynamic limit values for the scaled variances of neutral and charged pions are calculated. The enhancements of the fluctuations due to Bose statistics are found and discussed.