  We prove a duality between the asymmetric simple exclusion process (ASEP)
with non-conservative open boundary conditions and an asymmetric exclusion
process with particle-dependent hopping rates and conservative reflecting
boundaries. This is a reverse duality in the sense that the duality function
relates the measures of the dual processes rather than expectations.
Specifically, for a certain parameter manifold of the boundary parameters of
the open ASEP this duality expresses the time evolution of a family of shock
product measures with $N$ microscopic shocks in terms of the time evolution of
$N$ particles in the dual process. The reverse duality also elucidates some so
far poorly understood properties of the stationary matrix product measures of
the open ASEP given by finite-dimensional matrices.
