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In this article, we study the entropy squeezing and the nonlocal correlation between a nonlinear quantum system initially in the BGS (Barut-Girardello state) and 2LA (two-level atom). The numerical solution is used for solving the differential equations to obtain the density matrix. The relation between the atomic inversion, nonlocal correlation measured by the negativity and entropy are discussed. The effective of classical field and damping on the dynamical properties of the entanglement and entropy squeezing is examined. The results are shown that a high amount of classical field due to the entanglement reached to minimum values. Finally the proposed quantum system being more resistant to the damping effect in the absence of classical field than the presence of classical field. [ABSTRACT FROM AUTHOR]