Exploring Non-perturbative Corrections in Thermodynamics of Static Dirty Black Holes

This study presents an investigation into the thermodynamic properties of a dirty black hole immersed in a uniform electric field within the framework of the Einstein-Nonlinear Electrodynamics (ENE)-dilaton theory. The analysis delves into various thermodynamic aspects, including heat capacity, Helmholtz free energy, and internal energy, providing insights into the behavior of the black hole under the influence of the electric field. Furthermore, the article explores the intricate interplay between quantum effects and thermodynamic behavior through the examination of quantum-corrected entropy. The study aims to shed light on the non-perturbative corrections that arise in this complex system, offering a comprehensive understanding of the modified thermodynamics of dirty black holes within the specified theoretical framework.