The modified moment method, irreversible thermodynamics, and the nonlinear viscosity of a dense fluid

The extended Gibbs relation is derived for dense fluids in a nonequilibrium state from the kinetic equation for dense fluids proposed in a previous paper. The method used for derivation is basically the same as that used in the case of dilute (ideal) gases described by the Boltzmann equation. The extended Gibbs relation derived is, as it should be, in the same form as for ideal gases, but the evolution equations for macroscopic variables involved contain contributions due to molecular interactions. This derivation together with that of the corresponding relation for ideal gases previously reported provides us with a mathematical basis to study irreversible thermodynamics for systems at any nonequilibrium state without making the assumption of local equilibrium. The non-Newtonian viscosity is also studied for a dense fluid with the stationary solution of the evolution equation for stress tensor and viscosity formulas are obtained as extensions of the formulas for ideal gases reported previously.