Entropy exchange and entanglement in Jaynes-Cummings model with Kerr-like medium and intensity-depend coupling

► for the resonant case, the entropy exchange occurs, but this phenomenon is easily destroyed when the detuning is introduced. ► the Kerr-like medium and intensity-depend coupling are very helpful for improving the quality of entropy exchange. ► the value of lower bound of concurrence between the atomand the field can not only be weakened but also enhanced under the influence of Kerr-like medium, but as to the effect of intensity-depend coupling, the entanglement can only be weakened.