  The unitary operator corresponding to the classical canonical transformation
that connects a general closed system to an open system under adiabatic
conditions is found. The quantum invariant operator of the adiabatic open
system is derived from the unitary transformation of the quantum Hamiltonian of
the closed system. On the basis of these results, we investigate the evolution
of the general quantum adiabatic system and construct a revised adiabatic
theorem. The adiabatic theorem developed here exactly reduces to the well-known
Berry adiabatic theorem when the control parameter
