Isentropic process of Reissner-Nordstr\"om black holes: a possible excess of the entropy bound via a non-perturbative channel

We study the implications of an isentropic processes applied to a Reissner-Nordstr\"om black hole. This process is possible if a black hole absorbs a particle with a specific ratio of energy and charge. We show that such an absorption process is not classically allowed, not only in Einstein gravity but also in several modified gravity theories, indicating that this prohibition is quite generic. However, an isentropic absorption process is quantum mechanically allowed: the particle can penetrate the potential barrier on the event horizon. We compute the probability of this absorption process and compare it to that of semi-classical effects. Non-perturbatively, if this process is accumulated, it is possible that the entanglement entropy can be greater than its Bekenstein-Hawking entropy and violate the entropy-bound relation.