Exponential corrected thermodynamics of black holes

It has been reported that the black hole entropy is modified by an exponential term due to the non-perturbative corrections interpreted as quantum effects. We now find the impact of such modification on the black hole mass and other thermodynamics quantities. We find that the Schwarzschild black hole mass decreased by quantum corrections. Hence, we study exponential corrected thermodynamics and statistics of black holes by computing the partition function. We obtain the particular condition on the event horizon radius to satisfy the 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 the quantum correction on the Reissner-Nordstrom black hole is the black thermodynamics instability at quantum scales. Finally, we consider the most general case of charged AdS black hole and study the corrected thermodynamics.