Large-System Phase-Space Dimensionality Loss in Stationary Heat Flows
  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. 
Harald A. Posch and William G. Hoover