A statistical mechanical derivation of thermodynamically consistent hydrodynamic equations for simple dissipative fluids

In this paper, a statistical mechanical derivation of thermodynamically consistent fluid mechanical equations is presented for non-isothermal viscous molecular fluids. The coarse-graining process is based on the combination of key concepts from earlier works, including the Dirac-delta formalism of Irving and Kirkwood, the identity of statistical physical ensemble averages by Khinchin, and the Chapman-Enskog theory. The derivation (i) reveals the microscopic roots of the thermodynamic variational principles, (ii) provides the relevant non-equilibrium thermodynamic potentials as well as the constitutive relations, and (iii) guarantees the non-negativity of the entropy production rate.