  We study a small quantum system (e.g. a simplified model for an atom or
molecule) interacting with two bosonic or fermionic reservoirs (say, photon or
phonon fields). We show that the combined system has a family of stationary
states, parametrized by two numbers $T_1$, $T_2$ (``reservoir temperatures'').
If $T_1\neq T_2$, then these states are non-equilibrium, stationary states
(NESS). In the latter case we show that they have nonvanishing heat fluxes and
positive entropy production. Furthermore, we show that these states are
dynamically asymptotically stable. The latter means that the evolution with an
initial condition, normal with respect to any state where the reservoirs are in
equilibria at temperatures $T_1$ and $T_2$, converges to the corresponding
NESS. Our results are valid for the temperatures satisfying the bound
$\min(T_1, T_2) > g^{2+\alpha}$, where $g$ is the coupling constant and $0<
\alpha<1$ is a power related to the infra-red behaviour of the coupling
functions.
