= Affine Bloch equation
{c}
{title2=$\dot s=As+c$}
A time-independent <Lindblad equation> becomes an affine linear equation for the <Generalized Bloch representation>. If $\mathcal L(I)=\sum_d[V_d,V_d^\dagger]$, then $A_{mn}=\operatorname{Tr}(\sigma_m\mathcal L(\sigma_n))$ and $c_m=\operatorname{Tr}(\sigma_m\mathcal L(I))/N$ for traceless basis indices. The offset vanishes exactly when the dynamics are unital. Equilibria solve $As_*=-c$, and deviations evolve as $s(t)-s_*=e^{At}(s(0)-s_*)$.
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