Transport coefficients of quasi-particle models within a new relaxation time approximation of the Boltzmann equation

TL;DR

This paper introduces a new relaxation time approximation for the Boltzmann equation that accurately models QCD thermodynamics and preserves fundamental collision properties, providing insights into transport coefficients and entropy production.

Contribution

It develops a novel formulation of the relaxation time approximation that maintains collision term properties and background independence, advancing kinetic theory modeling of QCD.

Findings

Transport coefficients depend on the energy dependence of relaxation time.

Entropy production is consistent with the second law and independent of matching conditions.

The model accurately describes thermodynamic properties of QCD at zero chemical potential.

Abstract

We investigate the transport properties of a kinetic theory model that is tuned to describe the thermodynamic properties of QCD at zero chemical potential using a new formulation of the relaxation time approximation. In contrast to previous approaches, the latter is constructed to preserve the fundamental properties of the collision term of the Boltzmann equation for any energy-dependence of the relaxation time. A novel choice of matching conditions is implemented to ensure that the background mean-field depends only on the temperature even when the system is out of equilibrium. We provide a consistent analysis of how the transport coefficients of relativistic Navier-Stokes theory vary with the energy dependence of the relaxation time. We also show that the entropy production of this theory is consistent with the second law of thermodynamics and verify that it is independent of the matching conditions employed. We used this fact to calculate the matching independent combination of transport coefficients.