Heat transport in dielectric crystals at low temperature: A variational formulation based on extended irreversible thermodynamics

We propose a variational principle applicable to the heat-transport equations derived some years ago by Guyer and Krumhansl [Phys. Rev. 133, 1411 (1964); 148, 766 (1966); 148, 778 (1966)] to describe heat-wave propagation in dielectric crystals at low temperature. The variational principle appears as a generalization of Prigogine's minimum-entropy production criterion. The analysis is based on extended irreversible thermodynamics, which is used to derive the Guyer-Krumhansl equations from macroscopic arguments.