  A theoretical framework is proposed for an energy decomposition scheme along
the reaction coordinate, in which the ensemble average of the potential energy
weighted with reactive flux intensity is decomposed into energy components at
the per-coordinate level. The decomposed energy quantity is demonstrated to be
closely related to the free energy along the reaction coordinate and its
connection to the emergent potential energy is provided. We also explore the
property of the reactive flux weighted by the potential energy in the subspace
of collective variables. A free energy analogue is then proposed in the
subspace of collective variables and the directional derivative of this free
energy analogue in the direction of the reactive flux is shown to be useful in
the identification of the reaction coordinate and the minimum free energy path.
