  Within a closed system, physical interactions are reciprocal. However, the
effective interaction between two entities of an open system may not obey
reciprocity. Here, we describe a non-reciprocal interaction between
nanoparticles which is one-way, almost insensitive to the interparticle
distance, and scalable to many particles. The interaction we propose is based
on the non-conservative optical forces between two nanoparticles with highly
directional scattering patterns. However, we elucidate that scattering patterns
can in general be very misleading about the interparticle forces. We introduce
zeroth- and first-order non-reciprocity factors to precisely quantify the
merits of any optomechanical interaction between nanoparticles. Our proposed
one-way interaction could constitute an important step in the realization of
mesoscopic heat pumps and refrigerators, the study of non-equilibrium systems,
and the simulation of non-Hermitian quantum models.
