Some thoughts about nonequilibrium temperature

TL;DR

This paper argues that within kinetic theory, there is no evidence to modify the classical Fourier law by replacing temperature with a non-equilibrium temperature, challenging recent proposals in extended thermodynamics.

Contribution

It demonstrates that the traditional temperature remains valid in non-equilibrium steady states within the kinetic framework, countering recent claims for a non-equilibrium temperature.

Findings

No kinetic evidence supports replacing temperature with non-equilibrium temperature.

Classical Fourier law remains valid in non-equilibrium steady states.

Extended Irreversible Thermodynamics' temperature concept lacks kinetic foundation.

Abstract

The main objective of this paper is to show that, within the present framework of the kinetic theoretical approach to irreversible thermodynamics, there is no evidence that provides a basis to modify the ordinary Fourier equation relating the heat flux in a non-equilibrium steady state to the gradient of the local equilibrium temperature. This fact is supported, among other arguments, through the kinetic foundations of generalized hydrodynamics. Some attempts have been recently proposed asserting that, in the presence of non-linearities of the state variables, such a temperature should be replaced by the non-equilibrium temperature as defined in Extended Irreversible Thermodynamics. In the approximations used for such a temperature there is so far no evidence that sustains this proposal.