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Electrodynamics and rational thermodynamics

Müller, Ingo; Müller, Wolfgang H.

The electromagnetic fields (D, H) represent contravariant components of an antisymmetric 4‐tensor, while the fields (E, B) represent covariant components of the same 4‐tensor. Both sets are identical in Lorentz frames. The governing equations for them represent equations of balance for the flux of D and the flux B across open surfaces and they are invariant under arbitrary analytic transformation of space and time. This convenient property has motivated mechanicians to reformulate mechanics and thermodynamics in terms of the symmetric 4‐tensor of energy‐momentum so as to exhibit, perhaps, the same invariance as electromagnetism: general relativity. The interpretation of electromagnetism in terms of fields carries the theory a long way. But it breaks down when absorption and emission of radiation by bodies is concerned. In this case the proper view is that of a photon gas. Also the elegant union of electromagnetism and thermodynamics meets practical difficulties for bodies with internal structure, like electric and magnetic dipoles or for mixtures of charged constituents. The description of such bodies is limited to velocities much smaller than that of light. Still in those bodies the entropy inequality implies severe and interesting restrictions on the dependence of material properties on the electromagnetic fields. It will be evaluated by using the Lagrange multiplier method. In the early days of electromagnetism there was much confusion among physicists and engineers about the different formulation of the fields and about proper dimensions and units. This dilemma is also briefly explained in the article.
Published in: ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 10.1002/zamm.202300209, Wiley