Nonequilibrium temperature and thermometry in heat-conducting phi4 models.

We analyze temperature and thermometry for simple nonequilibrium heat-conducting models. We also show in detail, for both two- and three-dimensional systems, that the ideal-gas thermometer corresponds to the concept of a local instantaneous mechanical kinetic temperature. For the phi4 models investigated here the mechanical temperature closely approximates the local thermodynamic equilibrium temperature. There is a significant difference between the kinetic temperature and nonlocal configurational temperature. Neither obeys the predictions of extended irreversible thermodynamics. Overall, we find that the kinetic temperature, as modeled and imposed by the Nosé-Hoover thermostats developed in 1984, provides the simplest means for simulating, analyzing, and understanding nonequilibrium heat flows.