Variational theory for thermodynamics of thermal waves

We discuss description of macroscopic representations of thermal fields with finite signal speed by composite variational principles involving suitably constructed potentials along with original physical variables. A variational formulation for a given vector field treats all field equations as constraints that are linked by Lagrange multipliers to the given kinetic potential. We focus on the example of simple hyperbolic heat transfer, but also stress that the approach can be easily extended to the coupled transfer of heat, mass, and electric charge. With our approach, various representations may be obtained for physical fields in terms of potentials (gradient or non-gradient representations). Corresponding Lagrangian and Hamiltonian formalism can be developed. Symmetry principles yield components of the energy-momentum tensor for the given kinetic potential. The limiting reversible case appears as a special yet suitable reference frame to describe irreversible phenomena. With the conservation laws resulting from the least action principle and the Gibbs equation, the variational scheme of nonequilibrium thermodynamics follows. Its main property is abandoning the assumption of local thermal equilibrium.