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The Lindblad master equation for an arbitrary quadratic system of n fermionsis solved explicitly in terms of diagonalization of a 4n x 4n matrix, providedthat all Lindblad bath operators are linear in the fermionic variables. Themethod is applied to the explicit construction of non-equilibrium steady statesand the calculation of asymptotic relaxation rates in the far from equilibriumproblem of heat and spin transport in a nearest neighbor Heisenberg XY spin 1/2chain in a transverse magnetic field.

Third quantization: a general method to solve master equations for quadratic open Fermi systems