Observational analysis derives constitutive equations from Maxwell's equations and dissipation inequality in electromagnetic materials, suggesting foundational advancements.
For taking into account electromagnetic fields consistently we start out with a relativistic formulation of the balance equations of particle number, energy-momentum, and Maxwell's equations as well as the dissipation inequality. A state space including the electromagnetic field and the first derivatives of temperature and 4-velocity is introduced, and the dissipation inequality is exploited according to Liu's procedure - which in general contains that of Coleman-Noll as a special case. The constitutive equations of the class of material defined by the state space and some additional presuppositions as well as the remaining dissipation inequality are derived.
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Ellinghaus et al. (1991) studied this question.
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