Differences between Statistical Mechanics and Thermodynamics on the   Mesoscopic Scale
  We present a systematic expansion in the ratio between the level spacing and temperature and employ it to evaluate differences between statistical mechanics and thermodynamics in finite disordered systems. These differences are related to spectral correlations in those systems. They are fairly robust and are suppressed at temperatures much higher than the level spacing. 
Alex Kamenev and Yuval Gefen