No-go theorem in many body dissipative particle dynamics

TL;DR

This paper establishes a no-go theorem for multicomponent many body dissipative particle dynamics, revealing fundamental limitations on the force laws derivable from a potential due to integrability constraints.

Contribution

It introduces a no-go theorem that characterizes which density-dependent force laws in MDPD are physically realizable from a potential.

Findings

Not all density-dependent forces in MDPD are derivable from a potential.

The integrability condition imposes strong constraints on force laws.

The theorem guides the development of physically consistent MDPD models.

Abstract

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.