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In this paper, a statistical physical derivation of thermodynamicallyconsistent fluid mechanical equations is presented for non-isothermal viscousmolecular fluids. The coarse-graining process is based on (i) the adiabaticexpansion of the one-particle probability density function around LocalThermodynamic Equilibrium, (ii) the assumption of decoupled particle positionsand momenta, and (iii) the variational principle. It is shown that there existsa class of free energy functionals for which the conventional thermodynamicformalism can be naturally adopted for non-equilibrium scenarios, and describesentropy monotonic fluid flow in isolated systems. Furthermore, the analysis ofthe general continuum equations revealed the possibility of a non-localtransport mode of energy in highly compressible dense fluids.

Hydrodynamic Density Functional Theory of simple dissipative fluids