  We analyze the thermodynamics of the noncommutative high-dimensional
Schwarzschild-Tangherlini AdS black hole with the non-Gaussian smeared matter
distribution by regarding a noncommutative parameter as an independent
thermodynamic variable named as the noncommutative pressure. In the new
extended phase space that includes this noncommutative pressure and its
conjugate variable, we reveal that the noncommutative pressure and the original
thermodynamic pressure related to the negative cosmological constant make the
opposite effects in the phase transition of the noncommutative black hole, i.e.
the former dominates the UV regime while the latter does the IR regime,
respectively. In addition, by means of the reverse isoperimetric inequality, we
indicate that only the black hole with the Gaussian smeared matter distribution
holds the maximum entropy for a given thermodynamic volume among the
noncommutative black holes with various matter distributions.
