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Pure mathematics, Applied mathematics
A general tensor isothermal theory of free energies and free enthalpies for dielectrics is presented, corresponding to linear constitutive relations with memory. Starting from the general equations of continuum thermodynamics, various properties of and constraints on free energy/enthalpy functionals in dielectric media are noted. It is well-known that free enthalpies are particularly convenient in that their properties are closely analogous with those of free energies in mechanics, though different in crucial ways. General constitutive equations with memory are determined from a given free enthalpy. The form of the relaxation function, which occurs in these constitutive equations, is discussed from a general viewpoint. Also, various forms of the work function are given. Tensor formulae are derived for the minimum free energy and corresponding rate of dissipation for arbitrary and also sinusoidal histories of the electric and magnetic fields. Both the similarities with mechanics and the important differences, leading to different physical predictions, are emphasized throughout this work.
Glasgow S, Golden JM (2017) Dielectric Materials with Memory I: Minimum and General Free Energies. J At Nucl Phys 1(1):1-15.