Linked-cluster expansions in the equations of motion method for nonequilibrium processes

For an arbitrary irreversible process taking place in a closed physical system equations of motion are derived directly from the Liouville equation without introducing any projection operator. These equations are of nonmarkowian nature and are exactly valid for any system arbitrarily far from equilibrium. Using field-theoretical techniques the integral kernels in these equations are expanded into a diagram perturbation series which is proved to be linked. For a system having short memory it is shown that the secular divergent terms cancel each other. Then, using the diagram language the equations of motion are obtained in a much simpler form.