We study the non-perturbative quantum corrections to a Born–Infeld black hole in a spherical cavity. These quantum corrections produce a non-trivial short distances modification to the relation between the entropy and area of this black hole. The non-perturbative quantum correction appears as an exponential term in the black hole entropy. This in turn modifies the thermodynamics of a given system, for example reduced value of the Helmholtz free energy. Moreover, the first law of black hole thermodynamics modified due to quantum corrections. We also investigate the effect of such non-perturbative corrections on the information geometry of this system. This is done using some famous information metrics.

我们研究了球腔中玻恩-因菲尔德黑洞的非微扰量子校正。这些量子修正对这个黑洞的熵和面积之间的关系产生了非平凡的短距离修正。非微扰量子校正在黑洞熵中表现为指数项。这反过来又会改变给定系统的热力学，例如亥姆霍兹自由能的降低值。此外，由于量子校正，黑洞热力学第一定律发生了变化。我们还研究了这种非微扰校正对该系统的信息几何的影响。这是使用一些著名的信息指标完成的。