Heat conduction, and the lack thereof, in time-reversible dynamical systems: Generalized Nosé-Hoover oscillators with a temperature gradient

We use nonequilibrium molecular dynamics to analyze and illustrate the qualitative differences between the one-thermostat and two-thermostat versions of equilibrium and nonequilibrium (heat-conducting) harmonic oscillators. Conservative nonconducting regions can coexist with dissipative heat conducting regions in phase space with exactly the same imposed temperature field.