  The majority of quantum open system models in the literature are simplistic
in the sense that they only explicitly account for that part of the environment
that directly interacts with the system of interest. A quantum open system with
an open environment is examined using the projection operator method in the
weak coupling limit. The openness of environment is modelled by nonunitary
evolution of the Lindblad form. Under certain conditions, the resulting master
equation for the system is insensitive to the initial state of the environment
and to initial entanglements between the system and environment for time scales
greater than the environment relaxation timescales. For the particular case of
an environment consisting of a harmonic oscillator bath, the resulting master
equations are demonstrated to have the algebraic form for completely positive
evolution. The open environment model is illustrated for the particular case of
a system linearly coupled to an oscillator bath.
