Macroscopic spin and charge transport theory

According to the general principle of non-equilibriumthermodynamics, we propose a set of macroscopic transport equationsfor the spin transport and the charge transport. In particular, thespin torque is introduced as a generalized `current density' todescribe the phenomena associated with the spin non-conservation ina unified framework. The Einstein relations and the Onsagerrelations between different transport phenomena are established.Specifically, the spin transport properties of the isotropicnon-magnetic and the isotropic magnetic two-dimensional electrongases are fully described by using this theory, in which only themacroscopic-spin-related transport phenomena allowed by the symmetryof the system are taken into account.