  We address the question of how a non-equilibrium steady state (NESS) is
reached in the Linbdladian dynamics of an open quantum system. We develop an
expansion of the density matrix in terms of the NESS-excitations, each of which
has its own (exponential) decay rate. However, when the decay rates tend to
zero for many NESS-excitations (the spectral gap of the Liouvillian is closed
in the thermodynamic limit), the long-time dynamics of the system can exhibit a
power-law behaviour. This relaxation to NESS expectation values is determined
by the density of states close to zero spectral gap and the value of the
operator in these states. We illustrate this main idea on the example of the
lattice of non-interacting fermions coupled to Markovian leads at infinite bias
voltage. The current comes towards its NESS value starting from a typical
initial state as $\tau^{-3/2}$. This behaviour is universal and independent of
the space dimension.
