  Dissipative processes in non-equilibrium many-body systems are fundamentally
different than their equilibrium counterparts. Such processes are of great
importance for the understanding of relaxation in single molecule devices. As a
detailed case study, we investigate here a generic spin-fermion model, where a
two-level system couples to two metallic leads with different chemical
potentials. We present results for the spin relaxation rate in the nonadiabatic
limit for an arbitrary coupling to the leads, using both analytical and exact
numerical methods. The non-equilibrium dynamics is reflected by an exponential
relaxation at long times and via complex phase shifts, leading in some cases to
an "anti-orthogonality" effect. In the limit of strong system-lead coupling at
zero temperature we demonstrate the onset of a Marcus-like Gaussian decay with
{\it voltage difference} activation. This is analogous to the equilibrium
spin-boson model, where at strong coupling and high temperatures the spin
excitation rate manifests temperature activated Gaussian behavior. We find that
there is no simple linear relationship between the role of the temperature in
the bosonic system and a voltage drop in a non-equilibrium electronic case. The
two models also differ by the orthogonality-catastrophe factor existing in a
fermionic system, which modifies the resulting lineshapes. Implications for
current characteristics are discussed. We demonstrate the violation of
pair-wise Coulomb gas behavior for strong coupling to the leads. The results
presented in this paper form the basis of an exact, non-perturbative
description of steady-state quantum dissipative systems.
