Generalization of the Wall theorem to out-of-equilibrium conditions

The well-known Wall theorem states a simple and precise relation among temperature, pressure, and density of a fluid at contact with a confining hard wall in thermodynamic equilibrium. In this Communication, we develop an extension of the Wall theorem to out-of-equilibrium conditions, providing an exact relation between pressure, density, and temperature at the wall, valid for strong nonequilibrium situations. We derive analytically this nonequilibrium Wall theorem for stationary states and validate it with nonequilibrium event-driven molecular-dynamics simulations. We compare the analytical expression with simulations by direct evaluation of temperature, density, and pressure on the wall of a nanoconfined liquid under stationary flow. This is done for linear regime, medium and very strong out-of-equilibrium conditions, presenting viscous heating and heat transport. The agreement between theory and simulation is excellent, allowing for a conclusive verification. In addition, we explore the degree of accuracy of using the equilibrium Wall theorem and different expressions for the local temperature, employed in nonequilibrium molecular-dynamics simulations.