Meaningful timescales from Monte Carlo simulations of molecular systems with hard-core interactions

TL;DR

This paper introduces a novel Monte Carlo method for simulating molecular systems with hard-core interactions, establishing a direct link between simulation steps and real physical time, and validated against molecular dynamics.

Contribution

The paper presents a new rejection-free Markov Chain Monte Carlo approach that directly relates simulation steps to physical time for systems with hard-core interactions.

Findings

Converges to exact equilibrium and non-equilibrium dynamics

Reduces state transitions to a discrete set

Validated against event-driven molecular dynamics

Abstract

A new Markov Chain Monte Carlo method for simulating the dynamics of molecular systems characterized by hard-core interactions is introduced. In contrast to traditional Kinetic Monte Carlo approaches, where the state of the system is associated with minima in the energy landscape, in the proposed method, the state of the system is associated with the set of paths traveled by the atoms and the transition probabilities for an atom to be displaced are proportional to the corresponding velocities. In this way, the number of possible state-to-state transitions is reduced to a discrete set, and a direct link between the Monte Carlo time step and true physical time is naturally established. The resulting rejection-free algorithm is validated against event-driven molecular dynamics: the equilibrium and non-equilibrium dynamics of hard disks converge to the exact results with decreasing displacement size.