In this study, we explore the corrected thermodynamics of non-linear magnetic charged anti-de Sitter (AdS) black holes surrounded by quintessence, incorporating thermal fluctuations and deriving the corrected thermodynamic potentials. We analyze the effects of corrections due to thermal fluctuations on various thermodynamic potentials, including enthalpy, Helmholtz free energy, and Gibbs free energy. Our results show significant impacts on smaller black holes, with first-order corrections destabilizing them, while second-order corrections enhance stability with increasing parameter values. The specific heat analysis further elucidates the stability criteria, indicating that the large black holes ensure stability against phase transitions. However, the thermal fluctuations do not affect the physical limitation points as well as the second-order phase transition points of the black hole. Our findings highlight the intricate role of thermal fluctuations in black hole thermodynamics and their influence on stability, providing deeper insights into the behaviour of black holes under corrected thermodynamic conditions.

中文翻译：

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修正了被精髓包围的带磁 AdS 黑洞的热力学和稳定性


在这项研究中，我们探索了被精髓包围的非线性带磁反 de Sitter （AdS） 黑洞的校正热力学，结合了热波动并推导出校正后的热力学势。我们分析了热波动引起的校正对各种热力学势的影响，包括焓、亥姆霍兹自由能和吉布斯自由能。我们的结果表明，对较小的黑洞有显著影响，一阶校正会破坏它们的稳定性，而二阶校正会随着参数值的增加而增强稳定性。比热分析进一步阐明了稳定性标准，表明大黑洞确保了抗相变的稳定性。然而，热波动不会影响黑洞的物理限制点和二阶相变点。我们的研究结果强调了热波动在黑洞热力学中的复杂作用及其对稳定性的影响，为黑洞在校正热力学条件下的行为提供了更深入的见解。