\langle N_j^* \rangle ~+~ \sum_R ~\langle N_R \rangle
~\langle n_j \rangle_R~, \\
\langle \Delta N_j \Delta N_k \rangle ~&=~ \langle\left(\Delta N_j^*
\right)^2\rangle 
~\delta_{jk} ~+~\sum_{R} ~\langle (\Delta N_{R})^2 ~\rangle
\langle n_j \rangle_R\langle n_k \rangle_R~+~ \sum_{R} ~\langle
N_{R} ~\rangle \langle \Delta n_j \Delta n_k \rangle_R~,
\label{corr-id}\end{aligned}$$ where $N_j^*$ is primordial $j$th hadron multiplicity, and: $$\begin{aligned}
\langle n_j \rangle_R ~&=~ \sum_r ~b_r^R ~n_{j,R}^r ~,\\
 \langle \Delta n_j \Delta n_k \rangle_R~&=~ \langle n_j n_k
\rangle_R ~-\langle n_j\rangle_R \langle n_k\rangle_R ~=~ \sum_r
~b_r^R ~n_{j,R}^r ~n_{k,R}^r~-~\langle n_j \rangle_R\langle n_k \rangle_R~,\end{aligned}$$ $b_r^R$ is the branching ratio of the $r$th decay channel of $R$th resonance with normalization condition $\sum_r b_r^R=1$, while $n_{j,R}^r$ and $n_{k,R}^r$ are the respective multiplicities of particles of species $j$ and $k$ in $r$th decay channel of $R$th resonance. Generally, one finds enhancement of fluctuations due to resonance decay which leads to $\omega_j > 1$ (valid in GCE and CE, see, e.g., Ref. [@res_CE]). The first term in the right hand side of Eq. (\[corr-id\]) corresponds to fluctuation of $R$th resonance multiplicity and the second term appears due to the probabilistic character of resonance decay. For the Boltzmann gas discussed in this paper, it follows, $\langle (\Delta N_R)^2\rangle=\langle
N_R\rangle$, $\langle (\Delta N_j)^2\rangle=\langle
N_j^*\rangle$, and Eq. 