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The theory presented in part III of this series of articles [1], based on Informational Statistical Thermodynamics, provides a far-reaching generalization of the constitutive equations of Linear Irreversible Thermodynamics, recovering as a particular case the Maxwell-Cattaneo equations of Extended Irreversible Thermodynamics. Here we apply these results, as an illustrative example, to the case of a gas of free fermions interacting with a gas of free bosons, with the latter acting as a thermal bath. For the case of heat motion, propagation of damped second sound, or diffusive movement in the overdamped regime, is obtained

Microscopic Approach to Irreversible Thermodynamics IV: An Example of Generalized Diffusion and Wave Equations