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Quantum simulations basically rely on two kinetic theories which account for the coherent transport at different levels of approximation. These theories have complementary properties with respect to the ability to account for de-coherence processes, and become computationally expensive in describing mixed mode transport, where both, coherent and de-coherent processes must be taken into account. We consider an approach, where the coherent information, as provided by the non- equilibrium Green's function, is used in a kind of Wigner equation for the scattering induced correction to the coherent Wigner function. Here, we address the opportunity to approximate the equation by taking the classical limit in the Wigner potential term.