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In order to improve the finite element modeling of macroscopic eddy currents, a quadratic energy-based error criterion is obtained from a thermodynamic description of electromagnetism. Attention is first paid on the analytical derivation of the criterion in a general sense-i.e. without any assumption about the potential formulation and including possible body motion-especially to validate its relevance in 2D or 3D and to stress its independence from the formulation or the kind of application. Preliminary validation is given on a Thomson's effect device: As expected, the state functions provide the global convergence of the calculation within an iterative procedure whereas the conservation of the electromagnetic power is assessed locally to highlight the ill-checked elements.