Thermodynamics and phase transitions of nonlinear electrodynamics black holes in an extended phase space

We investigate the thermodynamic behavior of asymptotically AdS nonlinear electrodynamics (NLED) black holes in an extended phase space, where the cosmological constant Lambda = -3/l(2) is interpreted as a thermodynamic pressure. For a generic NLED black hole, we find that the Smarr relation is satis fied in the extended phase space if the dimensionful parameters in the NLED Lagrangian are considered as the thermodynamic variables. In a canonical ensemble with the charge Q fixed, we then investigate the phase structure and transitions of Born-Infeld AdS black holes, endowed with a parameter a > 0, which encodes the strength of the nonlinearities. In the a/l(2)-Q/l phase space, the phase diagrams are obtained, which provides a new viewpoint towards the black holes' phase structure and critical behavior. It shows that the critical line and the region, where a reentrant phase transition occurs, are both finite and terminated at some point. Through the continuation to a < 0, we extend the analysis to a new type of NLED black holes, dubbed iBorn-Infeld AdS black holes. For the iBorn-Infeld AdS black holes, the critical line and the reentrant phase transition region are semi-in finite and extend to Q/l=infinity. We also examine the thermal and electrical stabilities of the Born-Infeld and iBorn-Infeld AdS black holes.