Study of entropy production in Yang-Mills theory with use of Husimi function

TL;DR

This paper investigates the thermalization process in Yang-Mills theory by employing Husimi functions to define entropy, demonstrating that HW entropy increases over time and can be computed using semi-classical approximations.

Contribution

It introduces a novel numerical approach to calculate HW entropy in Yang-Mills theory using Husimi functions and semi-classical methods, confirming entropy growth during thermalization.

Findings

HW entropy is finite and increases over time in Yang-Mills fields.

Semi-classical approximation is feasible for early-stage heavy-ion collision systems.

Product ansatz reproduces HW entropy within 20% error in few-body systems.

Abstract

Understanding the thermalization process in a pure quantum system is a challenge in theoretical physics. In this work, we explore possible thermalization mechanism in Yang-Mills(YM) theory by using a positive semi-definite quantum distribution function called a Husimi function which is given by a coarse graining of the Wigner function within the minimum uncertainty. Then entropy is defined in terms of the Husimi function, which is called the Husimi-Wehrl(HW) entropy. We propose two numerical methods to calculate the HW entropy. We find that it is feasible to apply the semi-classical approximation with the use of classical YM equation. It should be noted that the semi-classical approximation is valid in the systems of physical interest including the early stage of heavy-ion collisions. Using a product ansatz for the Husimi function, which is confirmed to reproduce the HW entropy within 20% error (overestimate) for a few-body quantum system, we succeed in a numerical evaluation of HW entropy of YM fields and show that it surely has a finite value and increases in time.