  Aval et al. proved that starting from a critical configuration of a chip-
firing game on an undirected graph, one can never achieve a stable
configuration by reverse firing any non-empty subsets of its vertices. In this
paper, we generalize the result to digraphs with a global sink where reverse
firing subsets of vertices is replaced with reverse firing multi-subsets of
vertices. Consequently, a combinatorial proof for the duality between critical
configurations and superstable configurations on digraphs is given. Finally, by
introducing the concept of energy vector assigned to each configuration, we
show that critical and superstable configurations are the unique ones with the
greatest and smallest (w.r.t. the containment order), respectively, energy
vectors in each of their equivalence classes.
