  We study the thermodynamical properties of black holes when described as
gases of indistinguishable punctures with a chemical potential. In this
picture, which arises from loop quantum gravity, the black hole microstates are
defined by finite families of half-integers spins coloring the punctures, and
the near-horizon energy measured by quasi-local stationary observers defines
the various thermodynamical ensembles. The punctures carry excitations of
quantum geometry in the form of quanta of area, and the total horizon area
$a_\text{H}$ is given by the sum of these microscopic contributions. We assume
here that the system satisfies the Bose-Einstein statistics, and that each
microstate is degenerate with a holographic degeneracy given by
$\exp\big(\lambda a_\text{H}/\ell_\text{Pl}^2\big)$ and $\lambda>0$. We analyze
in detail the thermodynamical properties resulting from these inputs, and in
particular compute the grand canonical entropy. We explain why the requirements
that the temperature be fixed to the Unruh temperature and that the chemical
potential vanishes do not specify completely the semi-classical regime of large
horizon area, and classify in turn what the various regimes can be. When the
degeneracy saturates the holographic bound ($\lambda=1/4$), there exists a
semi-classical regime in which the subleading corrections to the entropy are
logarithmic. Furthermore, this regime corresponds to a Bose-Einstein
condensation, in the sense that it is dominated by punctures carrying the
minimal (or ground state) spin value $1/2$.
