The Matrix model, a driven state variables approach to non-equilibrium thermodynamics

One of the new approaches in non-equilibrium thermodynamics is the so-called matrix model of Jongschaap. In this paper some features of this model are discussed. We indicate the differences with the more common approach based upon internal variables and the more sophisticated Hamiltonian and GENERIC formulations. Applications to rheological models as well as transport phenomena and finally the connection with the general control system theory are discussed.