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This paper investigate the partial entropy changes of the field and the atom in a system of an atom interacting with a single quantized cavity field including acceptable kinds of nonlinearities of both the field and the intensity-dependent atom-field coupling. The work shows that the substantial entropy exchange can occur when the mixed state parameters of the atom and the average number of photons in the cavity are respectively bounded within certain parameter regimes, and the substantial entropy exchange is independent of the parameters of the non-linear medium, the intensity of non-linear coupling and detuning. It is also explored that the detuning leads to collapse-revival of the field and atomic partial entropy changes occurring.