Nonequilibrium Temperature in Non-Fourier Heat Conduction

Abstract

The definition of temperature is the foundation of thermodynamics. In extended irreversible thermodynamics (EIT) which goes beyond the classical one to be compatible with the non-Fourier heat conduction, the nonequilibrium temperature is defined. Based on the thermomass theory, it is shown that the static and stagnant pressures of the thermomass flow correspond to the static and stagnant temperatures, respectively. The stagnant temperature is higher than the static one due to the kinetic energy of thermomass. The static temperature is the real state variable, which is identical to the nonequilibrium temperature. It should be the criterion of thermodynamic equilibrium. The local entropy and internal energy densities should be represented by the static temperature. In this manner, the classical relation between entropy, internal energy, and temperature still holds. The derivation based on the phonon Boltzmann equation shows that the integral of the second-order expansion of the distribution function in the energy balance equation corresponds to the kinetic energy of thermomass, which leads to the difference between the static and stagnant temperatures.