PRL Abstract
Abstract
The non-equilibrium molecular dynamics generated by the
SLLOD algorithm (so called due to its association with the
DOLLS tensor algorithm (
D.J. Evans and G.P. Morriss, { Statistical Mechanics
of Nonequilibrium Liquids} (Academic, New York 1990))
for fluid flow is considered. It is
shown that, in the absence of time-dependent boundary conditions
(e.g. shearing boundary conditions via explicit
cell dynamics or Lees-Edwards boundary conditions),
a conserved energy, H' exists for the equations of motion. The
phase space distribution generated by SLLOD dynamics
can be explicitly derived from H'. In the case of a fluid
confined between two immobile boundaries undergoing planar Couette flow,
the phase space distribution predicts a linear velocity profile,
a fact which suggests the flow
is field driven rather than boundary driven. For a general flow in
the absence of time-dependent boundaries, it
is shown that the SLLOD equations are no longer canonical in the
laboratory momenta, and a modified form of the SLLOD dynamics
is presented which is valid arbitrarily far from equilibrium
for all boundary conditions. From an analysis of the conserved
energy for the new SLLOD equations in the absence of
time-dependent boundary conditions, it is shown that the correct local
thermodynamics is obtained. In addition, the idea of
coupling each degree of freedom in the system to a Nosé-Hoover
chain thermostat is presented as a means of efficiently generating
the phase space distribution.