From thermostatistic to Maxwell equations: A variational approach of electromagnetism

摘要

In this paper, Maxwell equations are derived from thermodvnamic principles. While divergence-free flux density is obtained everywhere from the stationarity of the Gibbs free energy, the Maxwell-Faraday equation and the Ohm's law with motion are obtained, in conductors, by assuming an adiabatic and reversible evolution of the field. Hence, Maxwell-Faraday equation may be extended in the dielectric region for any time-varying excitation. Besides, magnetic- and dielectric-behavior laws result from the convexity of the magnetic and electrostatic Gibbs potentials. Furthermore, the Laplace and Lorentz forces are obtained from virtual work principle. Extension to high frequencies is also proposed beyond the plasma pulsation of metal. At last, the consistency of the approach with Finite Element Method is emphasized in order to present farther integration of design tools dedicated to industrial and economic growth and ecological challenges.