Energy-conserving DPD and thermodynamically consistent Fokker–Planck​ equation

The original Fokker–Planck equation does not satisfy most balance equations of continuum mechanics. Dissipative particle dynamics (DPD) is an attempt to remedy the demerits of the Fokker–Planck equation. However, a desirable kinetic equation should satisfy the four balance equations of irreversible thermodynamics, i.e., the balance equations of mass, momentum, energy, and entropy. To the best of the author's knowledge, only the Boltzmann kinetics fulfills all the conditions. We suggest a modified Fokker–Planck equation that satisfies all the conditions without the assumption of DPD, the pairwise additivity of dissipative and random forces. Our formalism is expected to minimize the number of adjustable functions that must be used in DPD.