Coarse-Graining of Microscopic Dynamics into Mesoscopic Transient Potential Model

Abstract

We show that a mesoscopic coarse-grained dynamics model which incorporates the transient potential can be formally derived from an underlying microscopic dynamics model. As a microscopic dynamics model, we employ the overdamped Langevin equation. By utilizing the path probability and the Onsager-Machlup type action, we calculate the path probability for the coarse-grained mesoscopic degrees of freedom. The action for the mesoscopic degrees of freedom can be simplified by incorporating the transient potential. Then the dynamic equation for the mesoscopic degrees of freedom can be simply described by the Langevin equation with the transient potential (LETP). As a simple and analytically tractable approximation, we introduce additional degrees of freedom which express the state of the transient potential. Then we approximately express the dynamics of the system as the the combination of the LETP and the dynamics model for the transient potential. The resulting dynamics model has the same dynamical structure as the responsive particle dynamics (RaPiD) type models [W. J. Briels, Soft Matter 5, 4401 (2009)] and the multi-chain slip-spring type models [T. Uneyama and Y. Masubuchi, J. Chem. Phys. 137, 154902 (2012)]. As a demonstration, we apply our coarse-graining method with the LETP to a single particle dynamics in a supercooled liquid, and compare the results of the LETP with the molecular dynamics simulations and other coarse-graining models.

25 pages, 3 figures, to appear in Phys. Rev. E

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• Relaxation Functions of Ornstein-Uhlenbeck Process with Fluctuating Diffusivity
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Cited by in corpus (5)

• Anomalous statistics in the Langevin equation with fluctuating diffusivity: from Brownian yet non-Gaussian diffusion to anomalous diffusion and ergodicity breaking
• Coarse-Grained Simulation Model for Crystalline Polymer Solids by using Breakable Bonds
• Multi-chain slip-spring simulations with various slip-spring densities
• Comparison of Linear Viscoelastic Behaviors of Langevin- and Jump-Rouse Models
• Application of Projection Operator Method to Coarse-Grained Dynamics with Transient Potential