Damghan University Press Journal of Holography Applications in Physics 2783-4778 5 3 2025 09 18 Holographic Complexity and Residual Entropy of a Rotating BTZ Black Hole within Horndeski Gravity 31 49 498 10.22128/jhap.2025.991.1114 EN Fabiano Francisco Dos Santos Departamento de Física, Universidade Federal do Maranhão, São Luís, 65080-805, Brazil 0000-0001-5473-8797 Journal Article 2025 04 16 This work explores the holographic complexity and residual entropy of a rotating BTZ black hole within the framework of Horndeski gravity. The investigation is motivated by the need to understand the emission of information from black holes, encoded by quantum complexity, which persists even at zero temperature. Traditionally, black holes are considered to cease emitting information upon reaching zero temperature, yet our findings suggest a minimum level of information or minimal entropy. This challenges the classical notion of black hole death. Recent studies in the context of Horndeski gravity and the AdS/BCFT correspondence have identified a nonzero minimal entropy at zero temperature. Our work shows that complexity and entropy provide crucial insights into the information emission from black holes, extending beyond their classical death. These findings significantly affect our understanding of black hole thermodynamics and quantum information theory. https://jhap.du.ac.ir/article_498_cc508e705d13f501ea8b24c64e382385.pdf