In this paper, we study the time evolution of the entropies and the degree of entanglement in the mixed state for a multi-quanta JC model taking into consideration Stark shift and Kerr-like medium effect, we use a numerical method to investigate the time evolution of the partial entropy of the atom and field subsystem. This is done in the framework of themulti-quanta presses JCmodel with both the Stark shift and Kerr-likemedium effect added. Furthermore, we examine the effect of the superposition states and a statistical mixture of coherent states as an initial field on the entropies and entanglement. Our results show that the setting of the initial state play an important role in the evolution of the sub-entropies and entanglement.