Hamilton-Jacobi and quantum theory formulations of thermal-wave propagation under the dual-phase lagging model of heat conduction

Dual-phase lagging model is one of the most promising approaches to generalize the Fourier heat conduction equation, and it can be reduced in the appropriate limits to the hyperbolic Cattaneo–Vernotte and to the parabolic equations. In this paper it is shown that the Hamilton–Jacobi and quantum theory formulations that have been developed to study the thermal-wave propagation in the Fourier framework can be extended to include the more general approach based on dual-phase lagging. It is shown that the problem of solving the heat conduction equation can be treated as a thermal harmonic oscillator. In the classical approach a formulation in canonical variables is presented. This formalism is used to introduce a quantum mechanical approach from which the expectation values of observables such as the temperature and heat flux are obtained. These formalisms permit to use a methodology that could provide a deeper insight into the phenomena of heat transport at different time scales in media with inhomogeneous t...