Temperature of nonequilibrium steady-state systems

We determined the operational temperatures of nonequilibrium-molecular-dynamics (NEMD) systems by the recently developed thermometer [A. Baranyai, Phys. Rev. E 61, R3306 (2000)] and compared these values to the dynamic temperatures [H. H. Rough, Phys. Rev. Lett. 78, 772 (1997)] of the same systems. NEMD models use a synthetic thermostat, a numerical feedback procedure to remove the dissipative heat instantaneously. A consequence of this feedback is a splitting of the dynamic temperature. The kinetic part is different from the configurational part because the energy is removed through the momentum subspace of the system. In addition to this, these temperature values also vary with respect to the direction of the external perturbation. In the case of planar Couette flow and color flow, the isotropic operational temperatures of dense liquids are always closer to the configurational than to the kinetic temperatures. We show that the observed split and the pronounced directional dependence of the dynamic temperature is an artifact caused by the instantaneous feedback of NEMD models. Since relaxation of a preset difference between the kinetic and the configurational temperature is an order of magnitude faster than the relaxation of the heat flux vector, for models with realistic thermostas such a split must be very small. We argue that in real systems, even far from equilibrium, the operational temperature and both terms of the dynamic temperature must be practically identical and isotropic.