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\begin{aligned} \frac{\mathrm{d} q_i}{\mathrm{d} t} = H_i c_{p,i} + \sum_{j=0}^{N_{\text{comp}} - 1} k_{ij} c_{p,i} c_{p,j} - q_i && i = 0, \dots, N_{\text{comp}} - 1 \end{aligned}