Atomistic formulas for local properties in systems with many-body interactions.

Area of Science:

• Physics
• Physical Chemistry
• Materials Science

Background:

• Continuum models of energy and momentum transport rely on local densities and fluxes.
• Accurate derivation of these quantities from atomistic principles is crucial for understanding material properties.
• Existing methods may have limitations in handling complex many-body interactions.

Purpose of the Study:

• To derive atomistic formulas for local densities and fluxes in continuum transport descriptions.
• To present and analyze general methods for potential energy distribution among particles.
• To establish exact consequences of classical mechanics for heat flux, stress tensor, and transport equations.

Main Methods:

• Derivation of atomistic formulas based on definitions of densities.
• Application of classical mechanics equations.
• Analysis of two general methods for potential energy distribution.

Main Results:

• Exact atomistic formulas for local densities and fluxes.
• Formulas for heat flux and stress tensor derived from fundamental principles.
• Transport equations for energy and momentum established as direct consequences of mechanics.

Conclusions:

• The derived formulas and equations provide a rigorous foundation for continuum transport theories.
• The approach is valid for systems with general many-body interactions.
• This work bridges atomistic details with macroscopic transport phenomena.