For studying the entropy exchange between the subsystems of the interaction system of a atom with the field in a leaking cavity,an exact solution of the master equation that describes the system by using the method of super-operator is obtained.The influences of the intensity of the cavity-field,the dissipative coefficient of the cavity and the Stark shift between two atomic levels on the linear entropy are discussed.The results show that: the more intense the cavity-field is,the longer the persistent time of the exchange of the entropy between the cavity field with other sub-systems is.When the two-level Stark shifts between the atomic levels changes to enhance the coupling between the atom and the cavity field increased and the cavity dissipation coefficient remain unchanged,the entropy of the system speed up the exchange and the steady-state values of the entropy become smaller.