The compatibility of dual-phase-lag (DPL) heat conduction with the hypothesis of local thermodynamic equilibrium (LTE) and extended irreversible thermodynamic is investigated. The analysis is based on evaluating the entropy production rate (EPR) for a solid slab that is exposed to a sudden temperature gradient at its boundaries. In this regard, an analytical solution is presented for the first-order and second order approximations of the DPL model. It is shown that by extending the non-Fourier Cattaneo-Vernotte (C-V) wave model to the high-order DPL model, the unphysical values of the slab temperature that exist in the solution of C-V wave model cannot be generally eliminated. However, a set of phase lag times for the DPL model exist based on which these unphysical values can be omitted by increasing the diffusion versus the wavelike features. (C) 2016 Published by Elsevier Ltd.