  The stochastic differential equations for a model of dissipative particle
dynamics with both total energy and total momentum conservation in the
particle-particle interactions are presented. The corresponding Fokker-Planck
equation for the evolution of the probability distribution for the system is
deduced together with the corresponding fluctuation-dissipation theorems
ensuring that the ab initio chosen equilibrium probability distribution for the
relevant variables is a stationary solution. When energy conservation is
included, the system can sustain temperature gradients and heat flow can be
modeled.
