Thermal heat reservoirs via Gauss' principle of least constraint; Dissipation, chaos, and phase-space dimensionality loss in one-dimensional chains.

We use Gauss' principle of least constraint to impose different kinetic temperatures on the two halves of a periodic one-dimensional chain. The thermodynamic result is heat flow, as predicted by the Second Law of Thermodynamics. The statistical-mechanical result can be either a phase-space limit cycle or a strange attractor, depending on the chain length and the size of the temperature difference. We document the sensitivity of the Lyapunov spectrum and the underlying phase-space topology by varying the chain length and the size of the kinetic-temperature difference.