A new framework for computing a general local self-diffusion coefficient using statistical mechanics

TL;DR

This paper introduces a new, statistically rigorous framework for calculating local self-diffusion coefficients in inhomogeneous and nanoscale systems using modified Green-Kubo formulas derived from linear response theory.

Contribution

It presents a novel, general method for computing local diffusion coefficients based on statistical mechanics, applicable to small and inhomogeneous systems, validated through molecular simulations.

Findings

The new formulas agree with existing methods in large systems.

They are applicable to nanoscale and inhomogeneous systems.

Simulations confirm the validity of the theoretical expressions.

Abstract

Widely applicable, modified Green-Kubo expressions for the local diffusion coefficient ($D_l$) are obtained using linear response theory. In contrast to past definitions in use, these expressions are statistical mechanical results. Molecular simulations of systems with anisotropic diffusion and an inhomogeneous density profile confirm the validity of the results. Diffusion coefficients determined from different expressions in terms of currents and velocity correlations agree in the limit of large systems. Furthermore, they apply to arbitrarily small local regions, making them readily applicable to nanoscale and inhomogeneous systems where knowledge of $D_l$ is important.