  By using projection superoperators, we present a new derivation of the
quantum master equation first obtained by the Authors in Phys. Rev. E {\bf 68},
066112 (2003). We show that this equation describes the dynamics of a subsystem
weakly interacting with an environment of finite heat capacity and initially
described by a microcanonical distribution. After applying the rotating wave
approximation to the equation, we show that the subsystem dynamics preserves
the energy of the total system (subsystem plus environment) and tends towards
an equilibrium state which corresponds to equipartition inside the energy shell
of the total system. For infinite heat capacity environments, this equation
reduces to the Redfield master equation for a subsystem interacting with a
thermostat. These results should be of particular interest to describe
relaxation and decoherence in nanosystems where the environment can have a
finite number of degrees of freedom and the equivalence between the
microcanonical and the canonical ensembles is thus not always guaranteed.
