  Using a quantum generalization of the Onsager principle of microscopic
reversibility, the magnetization of a system in a non-equilibrium steady state
quantum dot is formulated as a response of the interaction energy to an
external field. This formulation permits a direct and compact computation of
the steady-state magnetization of a non-equilibrium quantum dot as a
differential of the interaction energy. Unlike the direct computation of the
magnetization using perturbative Keldysh methods, this approach does not
require the use of a point splitting procedure. Our results nevertheless
support earlier calculations made in the limit of zero field, and they support
the survival of strong coupling to arbitrarily large voltages, both at zero
field, and under the conditions where the chemical potential difference $eV$
becomes equal to the spin-flip energy in a field $eV = g \mu_{B}B$.
