Gradient dynamics and entropy production maximization

Gradient dynamics describes irreversible evolution by means of a dissipation potential, which leads to several advantageous features like Maxwell--Onsager relations, distinguishing between thermodynamic forces and fluxes or geometrical interpretation of the dynamics. Entropy production maximization is a powerful tool for predicting constitutive relations in engineering. In this paper, both approaches are compared and their shortcomings and advantages are discussed.