  Many body dissipative particle dynamics (MDPD) is a particle-based simulation
method in which the interaction potential is a sum of self energies depending
on locally-sampled density variables. This functional form gives rise to
density-dependent pairwise forces, however not all such force laws are
derivable from a potential and the integrability condition for this to be the
case provides a strong constraint. A strategy to assess the implications of
this constraint is illustrated here by the derivation of a useful no-go theorem
for multicomponent MDPD.
