  We propose a new prescription for evaluating a von Neumann entropy in the
initial stage of high-energy heavy-ion collisions utilizing the time evolution
of classical Yang-Mills (CYM) field: The von Neumann entropy is computed for
the quantum coherent states constructed so as to give the classical gluon
fields as the expectation values. The entropy is to be liberated when the
complete decoherence is achieved. As a demonstration, the time evolution of the
CYM dynamics is solved with an initial condition which mimics the Glasma state,
though in a non-expanding geometry; the Glasma state is characterized by the
longitudinal color-electric and -magnetic fields with gluon fields'
fluctuations around it. We find that the initial longitudinal fluctuations of
the fields play essential roles for the entropy production in two ways: First,
the field fluctuations at $t=0$ themselves act as a source of the von Neumann
entropy prepared before the time evolution. Second, the initial fluctuations
triggers field instabilities, and hence the larger the strength of them, the
more the entropy production at later time.
