Nonequilibrium electromagnetics: Local and macroscopic fields and constitutive relationships

Abstract

We study the electrodynamics of materials using a Liouville-Hamiltonian-based statistical-mechanical theory. Our goal is to develop electrodynamics from an ensemble-average viewpoint that is valid for microscopic and nonequilibrium systems at molecular to submolecular scales. This approach is not based on a Taylor series expansion of the charge density to obtain the multipoles. Instead, expressions of the molecular multipoles are used in an inverse problem to obtain the averaging statistical-density function that is used to obtain the macroscopic fields. The advantages of this method are that the averaging function is constructed in a self-consistent manner and the molecules can either be treated as point multipoles or contain more microstructure. Expressions for the local and macroscopic fields are obtained, and evolution equations for the constitutive parameters are developed. We derive equations for the local field as functions of the applied, polarization, magnetization, strain density, and macroscopic fields.

The Interaction of Radio-Frequency Fields with Dielectric Materials at Macroscopic to Mesoscopic Scales

“…(4) depends on time. This can be remedied by using an integrodifferential equation with restoring and driving terms [ 40 , 41 ].…”

“…Depolarization, demagnetization, thermal expansion, exchange, nonequilibrium, and anisotropy interactions can influence the dipole orientations and therefore the fields and the internal energy. In modeling the constitutive relations in Maxwell’s equations, we must express the material properties in terms of the macroscopic field, not the applied or local fields, and therefore we need to make clear distinctions between the interaction processes [ 40 ].…”

Transport of Heat and Charge in Electromagnetic Metrology Based on Nonequilibrium Statistical Mechanics

“…In the past, other researchers have developed nonequilibrium statistical mechanical theories by adding a source term to Liouville's equation [11], but the approach used in this paper does not require a source term. This approach has been used previously to study the microscopic time evolution of electromagnetic properties [12][13][14]. The theory can be formulated either quantum-mechanically or classically.…”

Electromagnetic Nanoscale Metrology Based on Entropy Production and Fluctuations

“…(12). For example, if the driving forces are the related Lagrange multipliers, −E p /k B T , −H m /k B T , and 1/k B T , we obtain the equation of motion of the polarization response ∂P/∂t, (see Baker-Jarvis et al [6,20]):…”

“…Oppenheim and Levine extended Robertson's work, included a more general initial condition, and studied a linear approximation to entropy evolution [13]. Projection-operator approaches have been used to study the microscopic time evolution of electromagnetic properties [19][20][21]. In Robertson's approach the full density operator ρ(t) equals a relevant canonical density operator σ(t) plus a relaxation correction term that accounts for irrelevant information.…”