Thermodynamics of Barrow Einstein-power-Yang-Mills AdS black hole in the restricted phase space

Due to quantum gravitational effects, Barrow proposed that the black hole horizon is "fractalized" into a sphereflake. Based on this idea, in this work we investigate the phase structure and stability of Einstein-Power-Yang-Mills (EPYM) AdS black holes in the restricted phase space, assuming the black hole event horizon has a fractal structure. From the first law of thermodynamics for EPYM AdS black holes in the restricted phase space, we find that the mass parameter should be interpreted as the internal energy. Moreover, the Smarr relation for this system in the restricted phase space is not a homogeneous function due to the fractal structure, which differs significantly from the corresponding relation in the extended phase space. The presence of a fractal structure can be regarded as a probe for phase transitions. Interestingly, for a fixed central charge in the EPYM AdS black hole system with a fractal structure, a supercritical phase transition also exists, similar to the case in the standard EPYM AdS black hole system. Furthermore, we investigate the effects of the fractal parameter triangle and non-linear Yang-Mills parameter gamma on the thermodynamical stability of this system are also investigated.