It is well known that when vacuum polarization emerges in quantum electrodynamics, the non-linear interaction between electromagnetic fields should be considered. Moreover, the corresponding field of non-linear electrodynamics can have important effects on black hole physics. In this work, we focus on the relationship between an observable quantity, that is, the shadow radius, and the first-order phase transition of non-linear charged AdS black holes in the framework of Einstein-power-Yang-Mills gravity. The results show that, under a certain condition, there exists a first-order phase transition from the viewpoint of both the shadow radius and horizon radius, which depend on temperature (or pressure). From the viewpoint of the shadow radius, the phase transition temperature is higher than that from the viewpoint of the horizon radius under the same condition. This may be due to the non-linear Yang Mills charge and the gravitational effect. This indicates that the shadow radius can be regarded as a probe to reveal the thermodynamic phase transition information of black holes. The thermal profiles of coexistent large and small black hole phases when the system is undergoing the phase transition are presented for two different values of the non-linear Yang Mills charge parameter: $ \gamma=1,\; 1.5 $ . Furthermore, the effects of the non-linear Yang Mills charge parameter on the shadow radius and thermal profile are investigated.
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