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We consider the thermodynamics of the Einstein-Power-Yang-Mills AdS blackholes in the context of the gauge-gravity duality. Under this framework, theNewton's gravitational constant and the cosmological constant are varied in thesystem. We rewrite the thermodynamical first law in a more extended formcontaining both the pressure and the central charge of the dual conformal fieldtheory, i.e., the restricted phase transition formula. A novel phenomenaarises: the dual quantity of pressure is the effective volume, not thegeometric one. That is leading to a new behavior of the Van de Waals-like phasetransition for this system with the fixed central charge: the supercriticalphase transition. From the Ehrenfest's scheme perspective, we check out thesecond-order phase transition of the EPYM AdS black hole. Furthermore theeffect of non-linear Yang-Mills parameter on these thermodynamical propertiesis also investigated.

Restricted phase space thermodynamics of Einstein-power-Yang-Mills AdS black hole