A variational principle for mass transport

TL;DR

This paper introduces a variational principle for mass transport in solids that unifies computational methods, offers a new physical interpretation, and enables error estimation for diffusion approximations in both amorphous and crystalline materials.

Contribution

It presents a diffusion-independent variational framework that unifies existing approaches and introduces a new physical perspective on the Green function.

Findings

Provides a universal variational principle for diffusion.

Enables error estimation for diffusion approximations.

Offers a new physical interpretation of the Green function.

Abstract

A variation principle for mass transport in solids is derived that recasts transport coefficients as minima of local thermodynamic average quantities. The result is independent of diffusion mechanism, and applies to amorphous and crystalline systems. This unifies different computational approaches for diffusion, and provides a framework for the creation of new approximation methods with error estimation. It gives a different physical interpretation of the Green function. Finally, the variational principle quantifies the accuracy of competing approaches for a nontrivial diffusion problem.