From Galilean covariance to Maxwell equations: A thermodynamic insight to electromagnetism

Galilean electromagnetism is derived from a thermodynamic approach. Attention is paid on the various regimes allowed by the quasi-static limit. It is emphasized that an abrupt transition exists between the QS-magnetic and the QS-electric regimes for which different gauge conditions on the potentials should be considered. Besides, due to its quadratic formulation, the approach is shown to be intrinsically multi-scaled and suitable for energy-based homogenization.