Relativistic transport theory for simple fluids at first order in the gradients: a stable picture

TL;DR

This paper derives a relativistic transport theory for simple fluids that ensures a stable equilibrium state, with heat flux expressed in terms of temperature and density gradients, aligning with classical thermodynamics.

Contribution

It presents a first-order relativistic transport framework where heat flux depends linearly on gradients, ensuring stability, and uses the BGK kinetic model for simplicity.

Findings

Heat flux is linearly related to temperature and density gradients.

The equilibrium state is stable under transverse velocity fluctuations.

The approach aligns relativistic transport with classical thermodynamics principles.

Abstract

In this paper we show how using a relativistic kinetic equation the ensuing expression for the heat flux can be casted in the form required by Classical Irreversible Thermodynamics. Indeed, it is linearly related to the temperature and number density gradients and not to the acceleration as the so called \textit{first order in the gradients} theories propose. Since the specific expressions for the transport coefficients are irrelevant for our purposes, the BGK form of the kinetic equation is used. Moreover, from the resulting hydrodynamic equations it is readily seen that the equilibrium state is stable in the presence of the spontaneous fluctuations in the transverse hydrodynamic velocity mode of the simple relativistic fluid. The implications of this result are thoroughly discussed.