Statistical Mechanics of Dissipative Particle Dynamics

TLDR

The authors derive the stochastic differential equations and corresponding Fokker–Planck equation for the Dissipative Particle Dynamics updating algorithm. A minor algorithmic modification is required to recover the Gibbs distribution, linking temperature to noise amplitude via a fluctuation–dissipation theorem, but the modified discrete DPD algorithm satisfies these predictions only when the time step is sufficiently small, underscoring the critical role of time discretisation.

Abstract

The stochastic differential equations corresponding to the updating algorithm of Dissipative Particle Dynamics (DPD), and the corresponding Fokker-Planck equation are derived. It is shown that a slight modification to the algorithm is required before the Gibbs distribution is recovered as the stationary solution to the Fokker-Planck equation. The temperature of the system is then directly related to the noise amplitude by means of a fluctuation-dissipation theorem. However, the correspondingly modified, discrete DPD algorithm is only found to obey these predictions if the length of the time step is sufficiently reduced. This indicates the importance of time discretisation in DPD.