can follow the evolution of the three components of the vector (\[C19\]):

\[C20\] $$\begin{aligned}
\mathbb{U}^{\mathrm{T}}\left( 0\right) \mathbb{C}_{1} &=&\left( 
\begin{array}{ccc}
228 & 125 & 207\end{array}\right) ,  \label{C20a} \\
\mathbb{U^{\mathrm{T}}}\left( 0\right) \mathbb{C}_{2} &=&\left( 
\begin{array}{ccc}
-136 & 110 & -48\end{array}\right) ,  \label{C20b} \\
\mathbb{U^{\mathrm{T}}}\left( 0\right) \mathbb{C}_{3} &=&\left( 
\begin{array}{ccc}
-67 & -74 & 141\end{array}\right) ,  \label{C20c}\end{aligned}$$

where $\lim_{n\rightarrow \infty }\mathbb{U}^{\mathrm{T}}\left( n\right) =\mathbb{U}^{\mathrm{T}}\left( 0\right) \mathbb{C}_{1} $ is the asymptotic component and $\mathbb{U^{\mathrm{T}}}\left( 0\right) \mathbb{C}_{l}\times
\exp \left( -n/T_{l}\right) $, $l=2,3$, are the components of the transient regimes that present negative numbers in some entries, although all the components of vectors $\mathbb{U}^{\mathrm{T}}\left( n\right) $ and $\mathbb{U}^{\mathrm{T}}\left( 0\right) \mathbb{C}_{1} $, Eqs. (\[C19\]) and (\[C20a\]), are positive. The sum of the components of $\mathbb{U}^{\mathrm{T}}\left( 0\right) \mathbb{C}_{1}$ is $560$ which corresponds to the conserved sum of the entries of the vector (\[C18a\]), whereas the sums of the components of the vectors (\[C20b\]) and (\[C20c\]), $\sum_{i=1}^{3}\left( \mathbb{U^{\mathrm{T}}}\left( 0\right) \mathbb{C}_{2}\right) _{i}=-74$ and $\sum_{i=0}^{3}\left( \mathbb{U^{\mathrm{T}}}\left( 0\right) \mathbb{C}_{3}\right) _{i}=0$ respectively, do not need to be necessarily positive, that we interpret as virtual distributions. As $n$ increases the components $\left( \mathbb{U^{\mathrm{T}}}\left( 0\right) \mathbb{C}_{l}\right) \exp \left( -n/T_{l}\right) $ go to zero due to the exponential decay factor and only the asymptotic vector, Eq. (\[C20a\]), survives.

**(4)** 