Entropy production and isotropization in Yang-Mills theory with use of quantum distribution function

TL;DR

This paper studies the thermalization process in Yang-Mills theory using Husimi-Wehrl entropy, revealing rapid entropy production linked to chaos and instability, and showing entropy saturation coincides with pressure isotropization in heavy ion collisions.

Contribution

It introduces a semiclassical approach to compute HW entropy in Yang-Mills theory, demonstrating its rapid production and saturation during thermalization, and compares it with chaos indicators.

Findings

HW entropy production rate exceeds chaos-based estimates

Entropy saturates when the system reaches a quasi-stationary state

Entropy saturation time aligns with pressure isotropization around 1 fm/c

Abstract

We investigate thermalization process in relativistic heavy ion collisions in terms of the Husimi-Wehrl (HW) entropy defined with the Husimi function, a quantum distribution function in a phase space. We calculate the semiclassical time evolution of the HW entropy in Yang-Mills field theory with the phenomenological initial field configuration known as the McLerran-Venugopalan model in a non-expanding geometry, which has instabilty triggered by initial field fluctuations. HW-entropy production implies the thermalization of the system and it reflects the underlying dynamics such as chaoticity and instability. By comparing the production rate with the Kolmogorov-Sina\"i rate, we find that the HW entropy production rate is significantly larger than that expected from chaoticity. We also show that the HW entropy is finally saturated when the system reaches a quasi-stationary state. The saturation time of the HW entropy is comparable with that of pressure isotropization, which is around $1$ fm/c in the present calculation in the non-expanding geometry.