Nonequilibrium Maxwell-Demon NEMD simulations of transport: I. Extrapolating shear viscosity to the hydrodynamic limit

Abstract

We present a Maxwell-Demon nonequilibrium molecular dynamics method for measuring the shear viscosity of a Lennard-Jones fluid. The simulation cell is divided into two regions of width $w$ in the $x$-direction, with particles free to move between the two sides. The Demon maintains equal and opposite regional average particle velocities in the $y$-direction ($\pm u_p$), by applying an acceleration $g_{total}$ that includes both total force balance and a correction for diffusion of particles across boundaries. The momentum relaxation rate needed to sustain the nonequilibrium steady state (NESS) is $\gamma=g_{total}/u_p$. We show that the driven velocity profile is not imposed point-wise in $x$ by the constraint, but is selected by the regional hydrodynamic response of the fluid. For this shear geometry, the measured NESS profile in Eulerian slabs is well represented by a piecewise parabolic form, reminiscent of planar Poiseuille flow. The parabolic profile estimates the kinematic viscosity from work done on the shearing fluid, $\nu_{para}=\gamma_{total}w^2/12$, as well as an entropy production estimate, derived from heat removal by the Nos\'e--Hoover thermostat that keeps each regional average temperature constant. For a representative run, the work and entropy routes agree to within $0.6\%$, confirming consistency between the mechanical work supplied by the Demon and the heat removed by the thermostat. Once NESS driving is removed, the parabolic velocity profile relaxes exponentially rapidly to sinusoidal, the natural transverse momentum-diffusion eigenmode. These results establish the Maxwell-Demon shear method as a direct NEMD route for obtaining shear viscosity from momentum diffusion, work, and entropy balances. Our results in 3D for increasing system size $N$ (the number of particles) demonstrate that shear viscosity approaches an asymptote (the hydrodynamic limit) as $1/\sqrt{N}$.