Fluctuation relations for spin currents

The fluctuation theorem establishes general relations between transport coefficients and fluctuations in nonequilibrium systems. Recently there has been much interest in quantum fluctuation relations for electric currents. Since charge carriers also carry spin, it is important to extend the fluctuation theorem to spin currents. We use the principle of microscopic reversibility to derive such theorem. As a consequence, we obtain a family of relations between transport coefficients and fluctuations of spin currents. We apply the relations to the spin Seebeck effect and rectification of spin currents. Our relations do not depend on a microscopic model and hence can be used to test the validity of theoretical approximations in spin-transport problems.