Causality in non-fourier heat conduction

We present a study of the causal response of non-Fourier heat conduction by introducing a dispersive generalized thermal susceptibility and show it obeys Kramers-Kronig relations. In particular, we discuss the Cattaneo-Vernotte and the dual-phase lag models. The constitutive equations are written as a linear response theory and determine the conditions for which the dual-phase lag model does not satisfy Kramers-Kronig relations. An alternative model is presented to describe non-Fourier transport using the similarity with the causal response of viscoelastic materials to avoid this unphysical issue.

Automated summary

This study investigates the causal response of non-Fourier heat conduction by introducing a dispersive generalized thermal susceptibility and demonstrates its adherence to Kramers-Kronig relations. Specifically, the Cattaneo-Vernotte and the dual-phase lag models are discussed. The constitutive equations are formulated as a linear response theory to determine the conditions under which the dual-phase lag model fails to satisfy Kramers-Kronig relations. An alternative model is proposed to describe non-Fourier transport, leveraging the similarity with the causal response of viscoelastic materials to overcome this unphysical issue.