Starting with the Kubo formula for electric conductivity we derive a set of equations that define the spin diffusion that is present when current is driven through inhomogeneous magnetic media. We show the spin accumulation, or nonequilibrium magnetization, attendant to charge transport through regions of inhomogeneous magnetization is governed by the same equations found in a thermodynamic approach to magnetoelectric transport.
Camblong, Horacio E., "Effective Internal Fields and Magnetization Buildup for Magnetotransport in Magnetic Multilayered Structures" (1994). Physics and Astronomy. 17.