Logarithm corrections and thermodynamics for Horndeski gravity like black holes

In this paper, we compute the Hawking temperature by applying quantum tunneling approach for the Horndeski like black holes. We utilize the semi-classical phenomenon and WKB approximation to the Lagrangian field equation involving generalized uncertainty principle (GUP) and compute the tunneling rate as well as Hawking temperature. For the zero gravity parameter, we obtain results consistent without correction parameter or original tunneling. Moreover, we study the thermal fluctuations of the considered geometry and examine the stable state of the system by heat capacity technique. We also investigate the behavior of thermodynamic quantities under the influence of thermal fluctuations. We observe from the graphical analysis, the corresponding system is thermodynamically stable with these correction terms.