  Mesoscopic particle based fluid models, such as dissipative particle
dynamics, are usually assumed to be coarse-grained representations of an
underlying microscopic fluid. A fundamental question is whether there exists a
map from microscopic particles in these systems to the corresponding
coarse-grained particles, such that the coarse-grained system has the same bulk
and transport properties as the underlying system. In this letter, we
investigate the coarse-graining of microscopic fluids using a Voronoi type
projection that has been suggested in several studies. The simulations show
that the projection fails in defining coarse-grained particles that have a
physically meaningful connection to the microscopic fluid. In particular, the
Voronoi projection produces identical coarse-grained equilibrium properties
when applied to systems with different microscopic interactions and different
bulk properties.
