Boltzmann-Equation Based Derivation of Balance Laws in Irreversible   Thermodynamics
  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. 
Liu Hong, Zaibao Yang, Yi Zhu, Wen-An Yong
cond-mat.stat-mech physics.flu-dyn