  The Kirchhoff-Helmholtz principle of least heat dissipation is applied in
order to derive the stationary state of the spin-Hall effect. Spin-accumulation
due to spin-orbit interaction, spin-flip relaxation, and electrostatic
interaction due to charge accumulation are treated on an equal footing. A
nonlinear differential equation is derived, that describes both surface and
bulk currents and spin-dependent chemical potentials. It is shown that if the
ratio of the spin-flip relaxation length over the Debye-Fermi length is small,
the stationary state is defined by a linear spin-accumulation potential and
zero pure spin-current.
