\begin{align}
    \dot{\rho_A}&=r_A(\eta)\rho_A,\\
    \intertext{where $r_A(\eta)=r_{A,1}\cdot \Theta(\eta_k-\eta)$ and $r_A(\eta)=r_{A,2}\cdot \Theta(\eta-\eta_k)\cdot \Theta(1-\eta)$.}
    \dot{\rho_B}&=r_B(\eta)\rho_B,\\
    \intertext{where $r_B(\eta)=r_{B,1}\cdot \Theta(\eta_k-\eta)$ and $r_B(\eta)=r_{B,2}\cdot \Theta(\eta-\eta_k)\cdot \Theta(1-\eta)$.}
    \dot{\eta}&=r_A(\eta)\rho_A+r_B(\eta)\rho_B.
\end{align}
