  Controlling interactions out of thermodynamic equilibrium is crucial for
designing addressable and functional self-organizing structures. These active
interactions also underpin collective behavior in biological systems. Here we
study a general setting of active particles in a bath of passive particles, and
demonstrate a novel mechanism for long range attraction between active
particles. The mechanism operates when the translational persistence length of
the active particle motion is smaller than the particle diameter. In this
limit, the system reduces to particles of higher diffusivity ("hot" particles)
in a bath of particles with lower diffusivity ("cold" particles). This
attractive interaction arises as a hot particle pushes cold particles away to
create a large hole around itself, and the holes interact via a depletion-like
attraction. Strikingly, the interaction range is more than an order of
magnitude larger than the particle radius, well beyond the range of
conventional depletion force. Although the mechanism occurs outside the
parameter regime of typical biological swimmers, the mechanism could be
realized in the laboratory.
