Thermodynamically consistent dissipative particle

The formalism of thermodynamically consistent dissipative particle dynamics represents a consistent discrete model for the Lagrangian fluctuating hydrodynamics. Equation (26.45)-Equation (26.46) conserve the mass, momentum, energy and volume. The irreversible (produced) entropy S is a strictly inerting function of time in the absence of fluctuations. Thermal fluctuations represented by F, S are consistently included, which lead to an increase of the entropy and to correct for the Einstein distribution function [31]. 

FIGURE 26.11 The schematics of coarse-graining idea realized by the top-down thermodynamically consistent DPD model. The Voronoi cell represents a fragment of continuum fluid. This fragment can be treated as a dissipative particle with variable mass, volume, temperature and entropy. The thermodynamically consistent DPD particles interact with forces dependent not only on their positions and velocities but on the current thermodynamic states of interacting particles as well. 

In order to bridge mesoscopic scales with the scales described by SPH technique, Serrano and Espanol [32] propose a new version of dissipative particle dynamics, the thermodynamically consistent DPD (TC-DPD). 

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