We consider a few conceptual questions on extended thermodynamics, with the aim to contribute to a higher contact between rational extended thermodynamics and extended irreversible thermodynamics. Both theories take a number of fluxes as independent variables, but they differ in the formalism being used to deal with the exploitation of the second principle (rational thermodynamics in the first one and classical irreversible thermodynamics in the second one). Rational extended thermodynamics is more restricted in the range of systems to be analysed, but it is able to obtain a wider number of restrictions and deeper specifications from the second law. By contrast, extended irreversible thermodynamics is more phenomenological, its mathematical formalism is more elementary, but it may deal with a wider diversity of systems although with less detail. Further comparison and dialogue between both branches of extended thermodynamics would be useful for a fuller deployment and deepening of extended thermodynamics. Besides these two approaches, one should also consider the Hamiltonian approach, formalisms with internal variables, and more microscopic approaches, based on kinetic theory or on non-equilibrium ensemble formalisms. This article is part of the theme issue 'Fundamental aspects of nonequilibrium thermodynamics'.
Keywords: entropy; extended thermodynamics; generalized transport equations; nanosystems; non-equilibrium thermodynamics; second law.