RESUMO
We consider the thermodynamics of the Einstein-power-Yang-Mills AdS black holes in the context of the gauge-gravity duality. Under this framework, Newton's gravitational constant and the cosmological constant are varied in the system. We rewrite the thermodynamic first law in a more extended form containing both the pressure and the central charge of the dual conformal field theory, i.e., the restricted phase transition formula. A novel phenomena arises: the dual quantity of pressure is the effective volume, not the geometric one. That leads to a new behavior of the Van de Waals-like phase transition for this system with the fixed central charge: the supercritical phase transition. From the Ehrenfest's scheme perspective, we check out the second-order phase transition of the EPYM AdS black hole. Furthermore the effect of the non-linear Yang-Mills parameter on these thermodynamic properties is also investigated.