Generalized energy-conserving dissipative particle dynamics revisited: Insight from the thermodynamics of the mesoparticle leading to an alternative heat flow model

Recently we introduced the generalized energy-conserving dissipative particle dynamics method (GenDPDE) [J. Bonet Avalos, M. Lísal, J. P. Larentzos, A. D. Mackie, and J. K. Brennan, Phys. Chem. Chem. Phys. 21, 24891 (2019)], which has been formulated for an emerging class of density- and temperature-dependent coarse-grain models. In the original work, GenDPDE was formulated to ensure a fundamental link is maintained with the underlying physical system at the higher resolution scale. In this paper, we revisit the formulation of the GenDPDE method, and rederive the particle thermodynamics to ensure consistency at the opposing scale extreme, i.e., between the local thermodynamics in the mesoscopic systems and the corresponding macroscopic properties. We demonstrate this consistency by introducing unambiguous, physically meaningful definitions of the heat and work, which lead to the formulation of an alternative heat flow model that is analogous to Fourier's law of heat conduction. We present further analysis of the internal, unresolved degrees-of-freedom of the mesoparticles by considering the thermodynamics of an individual mesoparticle within the GenDPDE framework. Several key outcomes of the analysis include: (i) demonstration that the choice of the independent variables alters the particle thermodynamic description; (ii) demonstration that the mesoscopic thermodynamic transformations introduce additional terms of the order of the size of the local fluctuations, which prevent an unambiguous definition of both the heat and work; (iii) an emphasis on the importance of the choice of the proper estimators of the thermodynamic properties that are embedded in the chosen thermodynamic description; and (iv) a clearly defined path for determining any thermodynamic quantity dressed by the fluctuations. The further insight provided by this deeper analysis is useful for both readers interested in the GenDPDE theoretical framework, as well as readers interested in the practical ramifications of the analysis, namely, the alternative heat flow model.

Figure 1

Equilibrium probability distributions for the van der Waals equation-of-state at initial system temperature $T=1.5$ and system particle density $\rho =0.5$: (top left) particle internal energy; (bottom left) particle temperature; (top right) particle momentum; (bottom right) local particle density. Dashed lines are the probability distributions given by Eqs. (90), (91), (89), and (92) in Ref. [1], respectively, while solid lines are determined from a GenDPDE simulation with the alternative heat flow model. Due to each of the particle momenta being nearly identical, the plots for each component are indistinguishable.

Figure 2

Equilibrium particle internal energy probability distribution from a GenDPDE simulation of mesoparticles fixed in space using a small constant-volume heat capacity $C_V=5k_B$, with initial system temperature $T=1.5$, system particle density $\rho =0.5$, and heat conductivity parameter $\kappa =1$. The theoretical distribution was determined from Eq. (65).