We continue, in this article, to develop the formalism of nonequilibrium thermodynamics in variational form. We prove that in the framework of progress variables, the Hamilton-Jacobi equation has always a simple solution, and we prove that this solution becomes a state function if and only if there is a thermodynamic equilibrium for the system. We study an inequality between the dissipation of energy and of information, and we discuss the notion of relative entropy. Finally we also study in detail the case of a system with one chemical species, where all the previous quantities can be calculated explicitly.