We investigate the relative thermodynamic stability of the 3×3, 5×5, 7×7, 9×9 and infinitely large structures related to the dimers-adatoms-stacking faults family of Si(111) surface reconstructions by means of first-principles calculations. Upon accounting for the vibrational contribution to the surface free energy, we find that the 5×5 structure is more stable than the 7×7 at low temperatures. While a phase transition is anticipated to occur at around room temperature, the 7 × 7 → 5 × 5 transformation upon cooling is hindered by the limited mobility of Si atoms. The results not only flag a crucial role of vibrational entropy in the formation of the 7 × 7 structure at elevated temperatures, but also point for its metastable nature below room temperature. [Pre-print published in Physical Review B 105 , 245306 (2022)]