  A method is proposed to describe Fermi or Bose systems coupled to one or
several heat baths composed of fermions and/or bosons. The method, called
Coupled Equations of Motion method, properly includes non-Markovian effects.
The approach is exact in the Full-Coupling approximation when only bosonic
particles are present in the system and baths. The approach provides an
approximate treatment when fermions are present either in the system and/or in
one or several environments. The new approach has the advantage to properly
respect the Pauli exclusion principle for fermions during the evolution. We
illustrate the approach for the single Fermi or Bose two-level system coupled
to one or two heat-baths assuming different types of quantum statistics
(Fermion or Bosons) for them. The cases of Fermi system coupled to fermion or
boson heat baths or a mixture of both are analyzed in details. With the future
goal to treat Fermi systems formed of increasing number of two-level systems
(Qubits), we discuss possible simplifications that could be made in the
equations of motion and their limits of validity in terms of the system--baths
coupling or of the initial heat baths temperatures.
