A general method of quantum-to-classical reduction of quantum dynamics is described. The key aspect of our method is the similarity transformation of the Liouvillian, which provides a new perspective. In conventional studies of quantum energy transport, the rotating wave approximation has frequently been regarded as an inappropriate approach because it causes the energy flow through the system to vanish. Our formulation elucidates why this unphysical result occurs and provides a solution for the problem. That is, not only the density matrix but also the physical quantity is to be transformed. Moreover, we show that quantum dynamics can be "exactly" replaced with classical equations for the calculation of the transport efficiency.