Thermodynamically admissible form for discrete hydrodynamics

We construct a discrete model of fluid particles according to a two generator formalism for nonequilibrium thermodynamics. The model has the form of smoothed particle hydrodynamics including correct thermal fluctuations. A slight variation of the model reproduces the dissipative particle dynamics model with any desired thermodynamic behavior. The resulting algorithms have the following properties: mass, momentum, and energy are conserved, entropy is a nondecreasing function of time, and the thermal fluctuations produce the correct Einstein distribution function at equilibrium.