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We study the dynamics of quantum memory assist entropy uncertainty for qutritsystem coupled to an environment modeled by random matrices. The results showthat the effect of relative coupling strength on entropy uncertainty isopposite in Markov region and non-Markov region, and the influence of a commonenvironment and independent environments in Markov region and non-Markov regionis also opposite. One can reduce the entropy uncertainty by decreasing relativecoupling strength or puting the system in two separate environments in theMarkov case. In the non-Markov case, the entropy uncertainty can be reduced byincreasing the relative coupling strength or by placing the system in a commonenvironment.

The dynamics of entropy uncertainty for qutrit system under the random telegraph noise