  We study stochastic particle systems that conserve the particle density and
exhibit a condensation transition due to particle interactions. We restrict our
analysis to spatially homogeneous systems on finite lattices with stationary
product measures, which includes previously studied zero-range or misanthrope
processes. All known examples of such condensing processes are non-monotone,
i.e. the dynamics do not preserve a partial ordering of the state space and the
canonical measures (with a fixed number of particles) are not monotonically
ordered. For our main result we prove that condensing homogeneous particle
systems with finite critical density are necessarily non-monotone. On finite
lattices condensation can occur even when the critical density is infinite, in
this case we give an example of a condensing process that numerical evidence
suggests is monotone, and give a partial proof of its monotonicity.
