Extended phase space thermodynamics of regular-AdS black hole

After obtaining an exact regular-AdS black hole resulting from the coupling of general relativity with nonlinear electrodynamics (NED), we explore the thermodynamics of the extended phase space, treating the cosmological constant ( Λ ) as the pressure ( P ) of the black holes and its conjugate as thermodynamic volume ( V ). Considering the NED parameter ( g ), we investigate the Hawking temperature, entropy, Gibb’s free energy and specific heat at the horizon radius. Due to the presence of NED charge, the black hole exhibits van der Waals-like phase transition instead of Hawking-Page phase transition, which could be observed through the G - T plots, which display a swallowtail pattern below the critical pressure, and it gives rise to second-order phase transitions when pressure attains its critical value. The first-order phase transition shares similarities with the liquid-gas phase transition. We determine the exact critical points and explore the influence of NED on P - V criticality, revealing that the isotherms undergo a liquid-gas-like phase transition for temperatures below its critical value T C , especially at lower T C . The identical critical exponent to that of the van der Waals fluid suggests that the NED does not alter the critical exponents, as observed in other arbitrary AdS black holes.