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Updated: May 10, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Coarse-grained Monte Carlo simulations of non-equilibrium systems
Xiao Liu1, John C Crocker, Talid Sinno
1Department of Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA.
Abstract:
We extend the scope of a recent method for generating coarse-grained lattice Metropolis Monte Carlo simulations [X. Liu, W. D. Seider, and T. Sinno, Phys. Rev. E 86, 026708 (2012); and J. Chem. Phys. 138, 114104 (2013)] from continuous interaction potentials to non-equilibrium situations. The original method has been shown to satisfy detailed balance at the coarse scale and to provide a good representation of various equilibrium properties in both atomic and molecular systems. However, we show here that the original method is inconsistent with non-equilibrium trajectories generated by full-resolution Monte Carlo simulations, which, under certain conditions, have been shown to correspond to Langevin dynamics. The modified coarse-grained method is generated by simultaneously biasing the forward and backward transition probability for every possible move, thereby preserving the detailed balance of the original method. The resulting coarse-grained Monte Carlo simulations are shown to provide trajectories that are consistent with overdamped Langevin (Smoluchowski) dynamics using a sequence of simple non-equilibrium examples. We first consider the purely diffusional spreading of a Gaussian pulse of ideal-gas particles and then include an external potential to study the influence of drift. Finally, we validate the method using a more general situation in which the particles interact via a Lennard-Jones interparticle potential.
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