  We discuss the thermodynamic limit in the canonical area ensemble used in
loop quantum gravity to model quantum black holes. The computation of the
thermodynamic limit is the rigorous way to obtain a smooth entropy from the
counting entropy given by a direct determination of the number of microstates
compatible with macroscopic quantities (the energy in standard statistical
mechanics or the area in the framework presented here). As we will show in
specific examples the leading behavior of the smoothed entropy for large
horizon areas is the same as the counting entropy but the subleading
contributions differ. This is important because these corrections determine the
concavity or convexity of the entropy as a function of the area.
