  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.
