Two continuum approaches to a wavelength-dependent description of heat conduction

Heat conduction in rigid solids is examined with the purpose of setting up a systematic thermodynamic description accounting for frequency- and wavelength-dependent phenomena. Such a scheme is exhibited in two versions, namely extended irreversible thermodynamics and hidden variable thermodynamics. Though starting from different assumptions, the two versions lead to the same practical conclusions, which in turn may be identified with Chester's microscopic results on high-frequency thermometry. Also a generalization compatible with discontinuity propagation is proposed.