Recently, it is reported that thermal fluctuations which are interpreted as
quantum effects, modify black holes entropy by an exponential term. We now find
the effect of such modification on black hole mass and other thermodynamics
quantities. We find that Schwarzschild black hole mass decreased by thermal
fluctuations. Hence, we study exponential corrected thermodynamics and
statistics of black holes by computing the partition function. We obtain
special condition on the event horizon radius to satisfy Smarr-Gibbs-Duhem
relation in the presence of quantum correction. As we know the Schwarzschild
black hole is unstable, while the effect of exponential correction is the
stability of 4D Schwarzschild black hole as well as the Schwarzschild-AdS
black hole at a small area. On the other hand, a 5D Schwarzschild black hole
is completely unstable. The effect of quantum correction on the
Reissner-Nordstr\"{o}m black hole is instability at quantum scales. Finally, we
consider the most general case of charged AdS black hole and study corrected
thermodynamics.Comment: 19 pages, 15 figure