= Resistive evolution of the magnetic second-moment tensor
{title2=$D_tM-LM-ML^T=\eta_m\nabla^2M-2\eta_m\partial_n\mathbf B\,\partial_n\mathbf B^T$}
For constant <magnetic diffusivity>, apply the product rule to $M_{ij}=B_iB_j$ and the incompressible <resistive induction equation>. The identity $\nabla^2(B_iB_j)=B_i\nabla^2B_j+B_j\nabla^2B_i+2\partial_nB_i\partial_nB_j$ proves the displayed formula. Omitting the gradient-product term gives the wrong tensor evolution. Its average generally requires information beyond the averaged <magnetic second-moment tensor>.
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