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No-go theorem in many body dissipative particle dynamics

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.