Schrödinger Equation for an Open System

We present a Schrödinger (Liouville) type of equation for a quantum open system. It has a correlated part, and various master equations may be its special cases. It also has significant applications to construct decoherence-free subspace for quantum computation. It is related to the original Schrödinger (Liouville) equation for the total system through a non-unitary similarity transformation. It is unnecessary for its correlated part to be self-adjoint, so there is a complex spectrum for the corresponding Hamiltonian (Liouvillian), which enables the time evolution of states to be asymetric. This shows just the correlation to produce evolution of world.