Nonequilibrium electromagnetics: Local and macroscopic fields and constitutive relationships

Area of Science:

• Statistical Mechanics
• Electrodynamics
• Materials Science

Background:

• Traditional electrodynamics often relies on macroscopic approximations or Taylor expansions.
• Microscopic and nonequilibrium systems present challenges for existing theoretical frameworks.
• Understanding material electrodynamics at molecular scales is crucial for advanced applications.

Purpose of the Study:

• To develop a Liouville-Hamiltonian-based statistical-mechanical theory for electrodynamics.
• To enable accurate modeling of microscopic and nonequilibrium systems.
• To provide a framework valid from molecular to submolecular scales.

Main Methods:

• Utilizes a Liouville-Hamiltonian-based statistical-mechanical approach.
• Employs an inverse problem to derive the statistical-density function from molecular multipoles.
• Avoids Taylor series expansion of charge density for multipole determination.

Main Results:

• Derives expressions for local and macroscopic electromagnetic fields.
• Develops evolution equations for constitutive parameters.
• Obtains equations for the local field based on various applied and material properties.

Conclusions:

• The developed theory offers a self-consistent method for constructing averaging functions.
• It allows for the treatment of molecules as point multipoles or with internal microstructure.
• Provides a robust framework for studying electrodynamics in complex materials and conditions.