  In this paper, we study the phase tranisions in the extended holographic
thermodynamics of Born-Infeld AdS black holes. The extended gravitational
thermodynamics of black holes is related to the thermodynamics of the dual
field theory by varying both cosmological constant and Newton's constant. With
topological analysis and numerical calculation, we find that the reentrant
large-small-large black hole phase transition still exists in $D=4$.
Interestingly, a similar reentrant phase transition is also observed in the
dual field theory, between the high-, low- and high-entropy thermal states. For
higher dimension $D>4$, only the van der Waals like phase transition is
observed, both in the bulk and the dual field theory.
