  A perturbative quantum master equation is derived for a system interacting
with its environment, which is more general than the ones derived before. Our
master equation takes into account the effect of the energy exchanges between
the system and the environment and the conservation of energy in a finite total
system. This master quantum describes relaxation mechanisms in isolated
nanoscopic quantum systems. In its most general form, this equation is
non-Markovian and a Markovian version of it rules the long-time relaxation. We
show that our equation reduces to the Redfield equation in the limit where the
energy of the system does not affect the density of state of its environment.
This master equation and the Redfield one are applied to a spin-environment
model defined in terms of random matrices and compared with the solutions of
the exact von Neumann equation. The comparison proves the necessity to allow
energy exchange between the subsystem and the environment in order to correctly
describe the relaxation in isolated nanoscopic total system.
