  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.
