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By generalizing the usual current density to a matrix with respect to spinvariables, a general equation of continuity satisfied by the density matrix andcurrent density matrix has been derived. This equation holds in arbitraryspin-orbit coupling systems as long as its Hamiltonian can be expressed interms of a power series in momentum. Thereby, the expressions of the currentdensity matrix and a torque density matrix are obtained. The current densitymatrix completely describes both the usual current and spin current as well;while the torque density matrix describes the spin precession caused by a totaleffective magnetic field, which may include a realistic and an effective onedue to the spin-orbit coupling. In contrast to the conventional definition ofspin current, this expression contains an additional term if the Hamiltonianincludes nonlinear spin-orbit couplings. Moreover, if the degree of the fullHamiltonian $\geq3$, then the particle current must also be modified in orderto satisfy the local conservation law of number.Comment: 9 page

Description of spin transport and precession in spin-orbit coupling systems and general equation of continuity