$$ \begin{equation} \boxed{\frac{dS}{dt} = \sum_{k=1}^{K} \dot{M}_k \hat{S}_k + \frac{\dot{Q}}{T} + \dot{S}_{gen}} \end{equation} $$
$$ \begin{equation} \boxed{S_{gen} \geq 0 \text{, and } \frac{dS}{dt} = 0 \text{ at equilibrium}} \end{equation} $$
$$ \begin{equation} \boxed{\frac{dS}{dt} = \sum_{k=1}^{K} \dot{M}_k \hat{S}_k + \frac{\dot{Q}}{T} + \dot{S}_{gen}} \end{equation} $$
$$ \begin{equation} \boxed{S_{gen} \geq 0 \text{, and } \frac{dS}{dt} = 0 \text{ at equilibrium}} \end{equation} $$