We investigate the thermodynamic behavior of nonlinear electrodynamics (NLED) black holes in an extended phase space, which includes the cosmological constant $\Lambda=-3/l^{ 2}$ and dimensionful couplings $a$ in NLED as thermodynamic variables. For a generic NLED black hole with the charge $Q$, we find that the Smarr relation is satisfied in the extended phase space, and the state of equation can be written as $Tl=\tilde{ T}\left( r_{ +}/l,Q/l,al^{ -c} \right) $, where $\left[ a\right] =L^{ c}$, and $T$ and $r_{ +}$ are the temperature and horizon radius of the black hole, respectively. For some values of $Q/l$ and $al^{ -c}$, the phase structure of the black hole is uniquely determined. Focusing on Born-Infeld and iBorn-Infeld AdS black holes, we obtain the corresponding phase diagrams in the $a/l^{ 2}$-$Q/l$ plane, which provides a new viewpoint towards the black holes' phase structure and critical behavior. For Born-Infeld black holes, the critical line and the region, where a reentrant phase transition occurs, in the $a/l^{ 2}$-$Q/l$ plane are both finite and terminate at $\left\{ \tilde{ a}_{ c}\text{ , }\tilde{ Q}_{ c}\right\} \simeq\left\{ 0.069\text{ , }0.37\right\} $. However for iBorn-Infeld black holes, the critical line and the reentrant phase transition region in the $a/l^{ 2}$-$Q/l$ plane are semi-infinite and extend to $Q/l=\infty$. We also examine thermal and electrical stabilities of Born-Infeld and iBorn-Infeld AdS black holes.
Categories: gr-qc hep-th