DPD was first proposed in order to recover the properties of isotropy (and Galilean invariance) that were broken in the so-called lattice-gas automata method [5]. In DPD, each body is regarded as a coarse-grained particle. These particles interact in a soft (and short-ranged) potential, allowing larger integration timesteps than would be possible in MD, while simultaneously decreasing the number of degrees of freedom required. As in Langevin dynamics, a thermostat consisting of well-balanced damping and stochastic terms is applied to each particle. However, unlike in Langevin dynamics, both terms are pairwise and the damping term is based on relative velocities, leading to the conservation of both the angular momentum and the linear momentum. The property of Galilean invariance (i.e., the dependence on the relative velocity) makes DPD a profile-unbiased thermostat (PUT) [6,7] by construction and thus it is an ideal thermostat for nonequilibrium molecular dynamics (NEMD) [8]. The momentum is expected to propagate locally (while global momentum is conserved) and thus the correct hydrodynamics is expected in DPD [8], as demonstrated previously in [9]. Due to the aforementioned properties, DPD has been widely used to recover thermodynamic, dynamical, and rheological properties of complex fluids, with applications in polymer solutions [10], colloidal suspensions [11], multiphase flows [12], and biological systems [13]. DPD has been compared with Langevin dynamics for out-of-equilibrium simulations of polymeric systems in [14], where as expected the correct dynamic fluctuations of the polymers were obtained with the former but not with the latter.
