  In this paper we propose a novel approach to construct macroscopic balance
equations and constitutive equations describing various irreversible phenomena.
It is based on the general principles of non-equilibrium thermodynamics and
consists of four basic steps: picking suitable state variables, choosing a
strictly concave entropy function, separating entropy fluxes and production
rates properly, and determining a dissipation matrix. Our approach takes the
advantage of both EIT and GENERIC formalisms, and shows a direct correspondence
with Levermore's moment closure hierarchies for the Boltzmann equation. This
result may put various macroscopic modeling approaches starting from the
general principles of non-equilibrium thermodynamics on a solid microscopic
foundation based on the Boltzmann equation.
