  Thermostated tethered harmonic lattices provide good illustrations of the
phase-space dimensionality loss which occurs in the strange-attractor
distributions characterizing stationary nonequilibrium flows. We use
time-reversible nonequilibrium molecular dynamics, with two Nose-Hoover
thermostats, one hot and one cold, to study a family of square heat-conducting
systems. We find a phase-space dimensionality loss which can exceed the
dimensionality associated with the two driving Nose-Hoover thermostats by as
much as a factor of four. We also estimate the dimensionality loss in the
purely Hamiltonian part of phase space. By measuring the projection of the
total dimensionality loss there we show that nearly all of the loss occurs in
the Hamiltonian part. Thus this loss, which characterizes the extreme rarity of
nonequilibrium states, persists in the large-system thermodynamic limit.
