A Case Study of Non-Fourier Heat Conduction Using Internal Variables and GENERIC

Applying simultaneously the methodology of Non-Equilibrium Thermodynamics with Internal Variables (NET-IV) and framework General Equation for Reversible-Irreversible Coupling (GENERIC), we demonstrate that, in heat conduction theories, entropy current multipliers can be interpreted as relaxed state variables. Fourier's law its various extensions -- Maxwell-Cattaneo-Vernotte, Guyer-Krumhansl, Jeffreys type, Ginzburg-Landau (Allen-Cahn) type ballistic-diffusive equations are derived both formulations. Along these lines, a comparison NET-IV GENERIC is also performed. Our results may pave way microscopic/multiscale understanding beyond-Fourier conduction, open new ways numerical simulations heat-conduction problems.