Thermodynamics of Higher Dimensional Charged Black Holes: Non-Perturbative Study

In this paper, we consider higher-dimensional charged black holes to study non-perturbative corrected thermodynamics. This correction is dominant when the black hole size decreases due to the Hawking radiation. The non-perturbative correction on the black hole entropy is proportional to the exponential of the original entropy with a negative sign. We calculate some thermodynamics quantities such as the internal Helmholtz free energies, and obtain the effect of the exponential correction. We study the first law of thermodynamics and investigate how it satisfies. We also study the stability of the black hole through specific heat analysis and investigate the possible phase transition. We find a second-order phase transition which is interpreted as the unstable/stable phase transition. Then, we find a first-order phase transition which make it unstable. Hence, the final stage of the Reissner-Nordstr"{o}m black holes may be an unstable phase which means that black hole evaporation at the quantum scale. It may be a cause that we never find a black hole in accelerators.