A Theoretical Examination of Diffusive Molecular Dynamics

TL;DR

This paper provides a mathematical framework for diffusive molecular dynamics using relative entropy, enhancing understanding of its algorithmic flexibility and differences from existing models, especially in vacancy diffusion.

Contribution

It introduces a relative entropy-based framework for diffusive molecular dynamics, clarifying its mathematical foundations and differences from prior formulations.

Findings

Framework based on relative entropy enhances algorithm interpretation.

Additional entropic terms are identified in vacancy diffusion modeling.

Comparison shows key differences with existing formulations.

Abstract

Diffusive molecular dynamics is a novel model for materials with atomistic resolution that can reach diffusive time scales. The main ideas of diffusive molecular dynamics are to first minimize an approximate variational Gaussian free energy of the system with respect to the mean atomic coordinates (averaging over many vibrational periods), and to then to perform a diffusive step where atoms and vacancies (or two species in a binary alloy) flow on a diffusive time scale via a master equation. We present a mathematical framework for studying this algorithm based upon relative entropy, or Kullback-Leibler divergence. This adds flexibility in how the algorithm is implemented and interpreted. We then compare our formulation, relying on relative entropy and absolute continuity of measures, to existing formulations. The main difference amongst the equations appears in a model for vacancy diffusion, where additional entropic terms appear in our development.