  Due to their aperiodic nature, quasicrystals are one of the least understood
phases in statistical physics. One significant complication they present in
comparison to their periodic counterparts is the fact that any quasicrystal can
be realized as an exponentially large number of different tilings, resulting in
a significant contribution to the quasicrystal entropy. Here, we use
free-energy calculations to demonstrate that it is this configurational entropy
which stabilizes a dodecagonal quasicrystal in a binary mixture of hard spheres
on a plane. Our calculations also allow us to quantitatively confirm that in
this system all tiling realizations are essentially equally likely, with
free-energy differences less than 0.0001$k_BT$ per particle -- an observation
that could be the related to the observation of only random tilings in soft
matter quasicrystals. Owing to the simplicity of the model and its available
counterparts in colloidal experiments, we believe that this system is a
excellent candidate to achieve the long-awaited quasicrystal self-assembly on
the micron scale.
