  In this work we investigate the late-time stationary states of open quantum
systems coupled to a thermal reservoir in the strong coupling regime. In
general such systems do not necessarily relax to a Boltzmann distribution if
the coupling to the thermal reservoir is non-vanishing or equivalently if the
relaxation timescales are finite. Using a variety of non-equilibrium formalisms
valid for non-Markovian processes, we show that starting from a product state
of the closed system = system + environment, with the environment in its
thermal state, the open system which results from coarse graining the
environment will evolve towards an equilibrium state at late-times. This state
can be expressed as the reduced state of the closed system thermal state at the
temperature of the environment. For a linear (harmonic) system and environment,
which is exactly solvable, we are able to show in a rigorous way that all
multi-time correlations of the open system evolve towards those of the closed
system thermal state. Multi-time correlations are especially relevant in the
non-Markovian regime, since they cannot be generated by the dynamics of the
single-time correlations. For more general systems, which cannot be exactly
solved, we are able to provide a general proof that all single-time
correlations of the open system evolve to those of the closed system thermal
state, to first order in the relaxation rates. For the special case of a
zero-temperature reservoir, we are able to explicitly construct the reduced
closed system thermal state in terms of the environmental correlations.
