The algorithm for the DPD fluid, the dynamics of which is conceptually a combination of molecular dynamics, Brownian dynamics and lattice gas automata, is designed for simulating rheological properties of complex fluids on hydrodynamic time scales. This paper calculates the equilibrium and transport properties (viscosity, self-diffusion) of the thermostated DPD fluid explicitly in terms of the system parameters. It is demonstrated that temperature gradients cannot exist, and that there is therefore no heat conductivity. Starting from the N-particle Fokker-Planck, or Kramers equation, we prove an H-theorem for the free energy, obtain hydrodynamic equations, and derive a non-linear kinetic equation (the Fokker-Planck-Boltzmann equation) for the single particle distribution function. This kinetic equation is solved by the Chapman-Enskog method. The analytic results are compared with numerical simulations.
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