  We examine the laws of thermodynamics and the weak cosmic censorship
conjecture in the normal and extended phase space of Born-Infeld-anti-de Sitter
black hole by considering a charged particle absorption. In the normal phase
space, the first and second law of thermodynamics as well as the weak cosmic
censorship are still valid. However, in the extended phase space, the second
law of thermodynamics is violated for double-horizon black holes and part of
single-horizon black holes. The first law of thermodynamics and the weak cosmic
censorship conjecture are still valid for all black holes. In addition, we find
that the shift of the metric function, which determines the locations of the
horizons, takes the same form at the minimum point in both the normal and
extended phase space, indicating that the weak cosmic censorship conjecture is
independent of the thermodynamic phase space.
