Transport in Electromagnetic Metrology Based on Nonequilibrium Statistical Mechanics
James R. Baker-Jarvis, Jack T. Surek
Current research is probing transport on ever smaller scales. Modeling of the electromagnetic interaction with nanoparticles or small collections of dipoles and its associated the energy transport and nonequilibrium characteristics requires a detailed understanding of transport properties. The goal of this paper is to use a nonequilibrium statistical-mechanical method, to obtain time-correlation functions and associated transport expressions in electromagnetic driving. This study will apply entropy and entropy production to electromagnetic measurements, determination of Boltzmann's constant and generalized temperature. We utilize the time-symmetric Zwanzig-Robertson statistical-mechanical theory to study the exact time evolution of relevant variables in the electromagnetic interaction with materials. In this exact statistical-mechanical theory, a generalized canonical-density is used to define an entropy in terms of a set of relevant variables and associated Lagrange multipliers. The entropy and its production rate are defined through the relevant variables. The influence of the nonrelevant variables enter the equations through the projection-like operator and they influence the entropy. The final equations for the entropy rate are exact in that they incorporate an exact solution to the quantum or classical Liouville's equation. We present applications to electrical and thermal conductivity, specific heat, generalized temperature, Boltzmann's constant, and noise. The analysis can either be performed classically or quantum-mechanically and there are only a few modifications in transferring between the approaches.
Constitutive relations, electromagnetics, entropy, nanoscale, statistical mechanics, temperature