Nonequilibrium Temperature and Thermometry in Heat-Conducting Phi-4 Models

Abstract

We analyze temperature and thermometry for simple nonequilibrium heat-conducting models. We 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 Phi-4 models investigated here the mechanical temperature closely approximates the local thermodynamic equilibrium temperature. There is a significant difference between kinetic temperature and the nonlocal configurational temperature. Neither obeys the predictions of extended irreversible thermodynamics. Overall, we find that 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.

20 pages with six figures, revised following review at Physical Review E

References in corpus (3)

• Measuring Nonequilibrium Temperature of Forced Oscillators
• Violations of local equilibrium and linear response in classical lattice theories
• Some thoughts about nonequilibrium temperature

Cited by in corpus (6)

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• 2D and 3D Dense-Fluid Shear Flows via Nonequilibrium Molecular Dynamics. Comparison of Time-and-Space-Averaged Tensor Temperature and Normal Stresses from Doll's, Sllod, and Boundary-Driven Shear Algorithms
• Shockwaves and Local Hydrodynamics; Failure of the Navier-Stokes Equations
• A Review of the System-Intrinsic Nonequilibrium Thermodynamics in Extended Space (MNEQT) with Applications
• Markovian Approximation for the Nosé--Hoover method and H-theorem
• Pressure and entropy of hard spheres in the weakly nonequilibrium heat-conduction steady state