Construction of non-Markovian coarse-grained models employing the Mori–Zwanzig formalism and iterative Boltzmann inversion

Abstract

We propose a new coarse-grained (CG) molecular simulation technique based on the Mori-Zwanzig (MZ) formalism along with the iterative Boltzmann inversion (IBI). Non-Markovian dissipative particle dynamics (NMDPD) taking into account memory effects is derived in a pairwise interaction form from the MZ-guided generalized Langevin equation. It is based on the introduction of auxiliary variables that allow for the replacement of a non-Markovian equation with a Markovian one in a higher dimensional space. We demonstrate that the NMDPD model exploiting MZ-guided memory kernels can successfully reproduce the dynamic properties such as the mean square displacement and velocity autocorrelation function of a Lennard-Jones system, as long as the memory kernels are appropriately evaluated based on the Volterra integral equation using the force-velocity and velocity-velocity correlations. Furthermore, we find that the IBI correction of a pair CG potential significantly improves the representation of static properties characterized by a radial distribution function and pressure, while it has little influence on the dynamic processes. Our findings suggest that combining the advantages of both the MZ formalism and IBI leads to an accurate representation of both the static and dynamic properties of microscopic systems that exhibit non-Markovian behavior.

Recent Progress towards Chemically-Specific Coarse-Grained Simulation Models with Consistent Dynamical Properties

“…Lei et al [71] subsequently demonstrated that a fictitious particle approach can be more rigorously connected to the GLE representation through a rational function approximation of the Laplace transform of the memory kernel. More recently, Karniadakis and coworkers [40,72] have pursued a similar auxiliary variable approach, to simplify the implementation of non-Markovian DPD. Although these studies consider models with coarser representations (one site for a cluster of Lennard-Jones particles or an entire star polymer), the results contain potentially useful lessons for coarse-graining at a higherresolution.…”

Systematic derivation of hybrid coarse-grained models

“…( 6)). Different ways to consider the friction matrix were reported [19,47] as well as to include memory effects in CG simulations, [37,[76][77][78].…”

Coarse-Grained Modelling Out of Equilibrium

“…In the context of modelling soft matter, the method of extending the state space by auxiliary variables in order to obtain Markovian dynamics is also frequently used [52,189,190,53,171,46,54,191]. In particular, for coarse-grained polymer models, as described in sec.…”