  The evolution of a composite closed system using the integral wave equation
with the kernel in the form of path integral is considered. It is supposed that
a quantum particle is a subsystem of this system. The evolution of the reduced
density matrix of the subsystem is described on the basis of the integral wave
equation for a composite closed system. The equation for the density matrix for
such a system is derived. This equation is nonlinear and depends on the history
of the processes in the closed system. It is shown that, in general, the
reduced density matrix trace does not conserve in the evolution processes
progressing in open systems and the procedure of the trace normalization is
necessary as the mathematical image of a real nonlocal physical process. The
wave function collapse and EPR correlation are described using this approach.
