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In this paper, we investigate the effects of non-perturbative quantum gravitational corrections on a quantum sized AdS black hole. It will be observed that these non-perturbative quantum gravitational corrections modify the stability of this black hole. We will use the non-equilibrium quantum thermodynamics to investigate the evaporation of this black hole between two states. We will analyze the effects of non-perturbative quantum gravitational corrections on this non-equilibrium quantum thermodynamics. We will explicitly obtain the quantum work distribution for this black hole, as it evaporates between two states. It will be observed that this quantum work distribution is modified due to non-perturbative quantum gravitational corrections.