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

Current research is probing transport on ever smaller scales. Modeling of the electromagnetic interaction with nanoparticles or small collections of dipoles and its associated 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 exact time-correlation functions, fluctuation-dissipation theorems (FD), heat and charge transport, and associated transport expressions under electromagnetic driving. We extend the time-symmetric Robertson statistical-mechanical theory to study the exact time evolution of relevant variables and entropy rate 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. Then the entropy production rate are defined through the relevant variables. The influence of the nonrelevant variables enter the equations through the projection-like operator and thereby influences the entropy. We present applications to the response functions for the electrical and thermal conductivity, specific heat, generalized temperature, Boltzmann’s constant, and noise. The analysis can be performed either classically or quantum-mechanically, and there are only a few modifications in transferring between the approaches. As an application we study the energy, generalized temperature, and charge transport equations that are valid in nonequilibrium and relate it to heat flow and temperature relations in equilibrium states.