  We suggest a new approach for transport through finite systems based on the
Liouville equation. By working in a basis of many-particle states for the
finite system, Coulomb interactions are taken fully into account and correlated
transitions by up to two different contact states are included. This latter
extends standard rate equation models by including level-broadening effects.
The main result of the paper is a general expression for the elements of the
density matrix of the finite size system, which can be applied whenever the
eigenstates and the couplings to the leads are known. The approach works for
arbitrary bias and for temperatures above the Kondo temperature. We apply the
approach to standard models and good agreement with other methods in their
respective regime of validity is found.
