  A multiscale theory of interacting continuum mechanics and thermodynamics of
mixtures of fluids, electrodynamics, polarization and magnetization is
proposed. The mechanical (reversible) part of the theory is constructed in a
purely geometric way by means of semidirect products. This leads to a complex
Hamiltonian system with a new Poisson bracket, which can be used in principle
with any energy functional. The thermodynamic (irreversible) part is added as
gradient dynamics, generated by derivatives of a dissipation potential, which
makes the theory part of the GENERIC framework. Subsequently, Dynamic MaxEnt
reductions are carried out, which lead to reduced GENERIC models for smaller
sets of state variables. Eventually, standard engineering models are recovered
as the low-level limits of the detailed theory. The theory is then compared to
recent literature.
