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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 timestep is sufficiently reduced. This indicates the importance of time discretisation in DPD. Recently, Hoogerbrugge and Koelman have introduced a new method for simulating hydrodynamic behavior which has been coined Dissipative Particle Dynamics (DPD)1,2. This technique was conceived as an improvement over conventional molecular dynamics MD in order to describe complex hydrodynamic behavior with c...
Español et al. (Mon,) studied this question.