ArticleEntropy (Basel, Switzerland)2024
An Entropy Dynamics Approach to Inferring Fractal-Order Complexity in the Electromagnetics of Solids.
Article in Entropy (Basel, Switzerland), 2024. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.
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Abstract
A fractal-order entropy dynamics model is developed to create a modified form of Maxwell's time-dependent electromagnetic equations. The approach uses an information-theoretic method by combining Shannon's entropy with fractional moment constraints in time and space. Optimization of the cost function leads to a time-dependent Bayesian posterior density that is used to homogenize the electromagnetic fields. Self-consistency between maximizing entropy, inference of Bayesian posterior densities, and a fractal-order version of Maxwell's equations are developed. We first give a set of relationships for fractal derivative definitions and their relationship to divergence, curl, and Laplacian operators. The fractal-order entropy dynamic framework is then introduced to infer the Bayesian posterior and its application to modeling homogenized electromagnetic fields in solids. The results provide a methodology to help understand complexity from limited electromagnetic data using maximum entropy by formulating a fractal form of Maxwell's electromagnetic equations.
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