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

TL;DR

This paper investigates temperature measurement in nonequilibrium heat-conducting Phi-4 models, showing that kinetic temperature aligns with local thermodynamic temperature, while configurational temperature does not, highlighting the effectiveness of Nosé-Hoover thermostats.

Contribution

It demonstrates that kinetic temperature accurately reflects local thermodynamic temperature in Phi-4 models, contrasting with configurational temperature, and emphasizes the utility of Nosé-Hoover thermostats for nonequilibrium heat flow analysis.

Findings

Kinetic temperature closely matches local thermodynamic temperature.

Configurational temperature significantly differs from kinetic temperature.

Nosé-Hoover thermostats effectively model nonequilibrium heat flows.

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 Nos\'e-Hoover thermostats developed in 1984, provides the simplest means for simulating, analyzing, and understanding nonequilibrium heat flows.