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

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