  We consider a finite quantum system S coupled to two environments of
different nature. One is a heat reservoir R (continuous interaction) and the
other one is a chain C of independent quantum systems E (repeated interaction).
The interactions of S with R and C lead to two simultaneous dynamical
processes. We show that for generic such systems, any initial state approaches
an asymptotic state in the limit of large times. We express the latter in terms
of the resonance data of a reduced propagator of S+R and show that it satisfies
a second law of thermodynamics. We analyze a model where both S and E are
two-level systems and obtain the asymptotic state explicitly (lowest order in
the interaction strength). Even though R and C are not direcly coupled, we show
that they exchange energy, and we find the dependence of this exchange in terms
of the thermodynamic parameters.
  We formulate the problem in the framework of W*-dynamical systems and base
the analysis on a combination of spectral deformation methods and repeated
interaction model techniques. We do not use master equation approximations.
