David Jou i Mirabent, José Casas Vázquez
The search for generalized heat transport equations describing Fourier’s diffusive regime is a frontier in nanoscale technology and energy management, together with thermal waves, Ziman regime, phonon hydrodynamics, and ballistic heat transport, as well as their respective transitions. Here we discuss the close connection between this search and another, much less known aspect, namely, the exploration of new forms of entropy and of the second law of thermodynamics for fast and steep perturbations and high values of heat flux, which would make generalized transport equations compatible with the second law. We also draw several analogies between this situation and the confluence of Fourier and Carnot theories that resulted in a general formulation during the foundational period of thermodynamics. [Contrib Sci 11(2): 131-136 (2015)]
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