  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.

General Relativity and Quantum Cosmology;High Energy Physics - Theory