Variational Principle for Mass Transport

Area of Science:

• Solid-state physics
• Materials science
• Computational physics

Background:

• Mass transport in solids is crucial for material properties and performance.
• Existing computational methods for diffusion often lack a unifying theoretical framework.
• Understanding diffusion mechanisms is key to designing new materials.

Purpose of the Study:

• To derive a general variation principle for mass transport in solids.
• To unify diverse computational approaches for diffusion modeling.
• To provide a framework for developing new approximation methods with error estimation.

Main Methods:

• Derivation of a variation principle for mass transport.
• Recasting transport coefficients as minima of local thermodynamic average quantities.
• Demonstration of independence from specific diffusion mechanisms.

Main Results:

• A unified variational principle applicable to both amorphous and crystalline solids.
• Transport coefficients are expressed as minima of local thermodynamic averages.
• The principle provides a new physical interpretation of the Green function.
• Quantification of the accuracy of competing diffusion approaches.

Conclusions:

• The derived variational principle offers a unified and general approach to mass transport in solids.
• This framework facilitates the development of novel, error-quantified approximation methods for diffusion.
• The principle provides new physical insights into transport phenomena and computational methods.