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We discuss the thermodynamic limit in the canonical area ensemble used inloop quantum gravity to model quantum black holes. The computation of thethermodynamic limit is the rigorous way to obtain a smooth entropy from thecounting entropy given by a direct determination of the number of microstatescompatible with macroscopic quantities (the energy in standard statisticalmechanics or the area in the framework presented here). As we will show inspecific examples the leading behavior of the smoothed entropy for largehorizon areas is the same as the counting entropy but the subleadingcontributions differ. This is important because these corrections determine theconcavity or convexity of the entropy as a function of the area.

The thermodynamic limit and black hole entropy in the area ensemble