 Resistive evolution of the magnetic second-moment tensor

For constant magnetic diffusivity, apply the product rule to $M_{ij}=B_i{B}_j$ and the incompressible resistive induction equation. The identity ${\nabla }^2(B_i{B}_j)=B_i{\nabla }^2{B}_j+B_j{\nabla }^2{B}_i+2{\partial }_n{B}_i{\partial }_n{B}_j$ 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.