Abstract
The goal in this paper is to show how many high-frequency electromagnetic metrology areas can be understood and formulated in terms of entropy evolution, production, and fluctuations. This may be important in nanotechnology where an understanding of fluctuations of thermal and electromagnetic energy and the effects of nonequilibrium are particularly important. The approach used here is based on a new derivation of an entropy evolution equation using an exact Liouville-based statistical-mechanical theory rooted in the Robertson-Zwanzig-Mori formulations. The analysis begins by developing an exact equation for entropy rate in terms of time correlations of the microscopic entropy rate. This equation is an exact fluctuation-dissipation relationship. We then define the entropy and its production for electromagnetic driving, both in the time and frequency domains, and apply this to study dielectric and magnetic material measurements, magnetic relaxation, cavity resonance, noise, measuring Boltzmann’s constant, and power measurements.
Highlights
The goal of this paper is to systematically analyze dynamically-driven, electromagnetic systems by starting from a detailed microscale theory and progress to various approximations and show how a wide array of electromagnetic metrology problems relate to entropy, entropy-production rate, and entropy rate fluctuation-dissipation relationships
The formalism and equations are derived for the entropy and its related evolution under electromagnetic driving
We know that changes in entropy satisfy δS = δQ/T + δSi, where δQ is the generalized heat added to the system, such as heat flowing in through the system boundaries and δSi is the entropy change due to irreversible processes such as relaxation
Summary
The goal of this paper is to systematically analyze dynamically-driven, electromagnetic systems by starting from a detailed microscale theory and progress to various approximations and show how a wide array of electromagnetic metrology problems relate to entropy, entropy-production rate, and entropy rate fluctuation-dissipation relationships. In the projection-operator approach used in this paper, a Gibbs-like relevant canonical-density operator σ(t) is constructed by maximizing the entropy subject to relevant constraint information This projection-operator approach, developed by Robertson [9], marries the Jaynes information-theoretic approach to the exact solution of the equations of motion by accounting for both relevant and irrelevant information. It is this correction term that relates to relaxation and is absent in the Jaynes information-theoretic and Gibbsian approaches. A new, very general and exact relation is derived for the entropy rate in terms of fluctuations in the microscopic entropy, an exact entropydensity equation is developed that includes entropy flux and production We apply this entropy expression in various linear approximations to describe electromagnetic applications. The fundamental results derived here are valid both at equilibrium or far from thermal or electrodynamic equilibrium and form a basis for extending measurements into the nanoscale and nonequilibrium realms
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