  We develop the thermodynamics of BPS and near-BPS AdS6 black holes. We study
the phase diagram of BPS black holes in the grand canonical ensemble. We
highlight two distinct deformations orthogonal to the BPS surface: (i)
increasing the temperature while keeping the charges fixed, (ii) changing the
charges while maintaining extremality such that the BPS constraint is no longer
satisfied. For both these deformations, we show that the considerations of the
BPS entropy function can be extended to describe the near-BPS regime. The
excess entropy together with changes in all potentials are perfectly accounted
for via the extremization principle.
