Pressure tensor and heat flux vector for inhomogeneous nonequilibrium fluids under the influence of three-body forces

We present a derivation of the pressure tensor and heat flux vector for inhomogeneous fluids under the influence of three-body forces. The derivation is based on the method of planes formalism of Todd, Evans, and Daivis [Phys. Rev. E 52, 1627 (1995); 51, 4362 (1995]. Our derivation is validated against nonequilibrium molecular dynamics simulations of a confined fluid acted upon by a two-body Barker-Fisher-Watts force coupled with the Axilrod-Teller three-body force. Our method of planes calculations agree perfectly with the equivalent mesoscopic route of integrating the momentum and energy continuity equations directly from the simulation data. Our calculations reveal that three-body forces have an important consequence for the isotropic pressure, but have negligible influence on the shear stress (hence viscosity)! and heat flux vector (hence thermal conductivity) for a confined simple fluid.