Effects of Structural Inhomogeneity on Equilibration Processes in Langevin Dynamics

TL;DR

This paper explores how initial inhomogeneities in molecular simulations affect relaxation times in Langevin dynamics, deriving a new relation between relaxation time and the radial distribution function, revealing longer equilibration for inhomogeneous states.

Contribution

It introduces an original expression linking relaxation time and radial distribution function, highlighting the impact of initial inhomogeneity on equilibration in Langevin systems.

Findings

Inhomogeneous initial states lead to longer relaxation times.

Relaxation time increases with Langevin coupling constant.

g(r) approaches 1 differently for homogeneous and inhomogeneous states.

Abstract

In recent decades, computer experiments have led to an accurate and fundamental understanding of atomic and molecular mechanisms in fluids, such as different kinds of relaxation processes toward steady physical states. In this paper, we investigate how exactly the configuration of initial states in a molecular-dynamics simulation can affect the rates of decay toward equilibrium for the widely-known Langevin canonical ensemble. For this purpose, we derive an original expression relating the system relaxation time {\tau}_{sys} and the radial distribution function g(r) in the near-zero and high-density limit. We found that for an initial state which is slightly marginally inhomogeneous in the number density of atoms, the system relaxation time {\tau}_{sys} is much longer than that for the homogeneous case and an increasing function of the Langevin coupling constant, {\gamma}. We also found during structural equilibration, g(r) at large distances approaches 1 from above for the inhomogeneous case and from below for the macroscopically homogeneous one.