Damghan University Press Journal of Holography Applications in Physics 2783-4778 3 2 2023 06 01 Holographic dual picture of a modified Horndeski black hole 17 30 303 10.22128/jhap.2023.565.1028 EN Naveed Ahmad Shah Department of Physics, Jamia Millia Islamia, New Delhi - 110025, India Abrar Ahmed Naqash Department Of Physics, National Institute Of Technology Srinagar, Jammu and Kashmir 190006, India Atif Kaisar Khan Department of Metallurgy and Materials Engineering, National Institute of Technology Srinagar, Jammu and Kashmir 190006, India Rameez Farooq Shah Department of Physics, Jamia Millia Islamia, New Delhi - 110025, India Suhail Ahmad Lone Department of Physics and Astrophysics, University of Delhi, Delhi 110007, India Journal Article 2022 06 20 The usual Horndeski black hole do not have $ P-V $ critical points, hence do not show any phase transitions. In this article we a particular modified Horndenski black hole is considered to study the $ P-V $ diagram and the phase transitions. We show that this modified Horndeski black hole solution satisfies the textit{Ist} order phase transition. We also show that the modified Horndeski black hole is holographic dual of a textit{Van der Waals}(VdW) fluid. Finally, we study the thermodynamics of modified Horndeski black hole based on the equation of state originating from the slope of temperature versus entropy. This new prescription provides us a simple and powerful way to study the critical behavior and the phase transition of black holes. The analytical interpretation of possible phase transition points leads us to set some nonphysical range on the horizon radius for the black hole. https://jhap.du.ac.ir/article_303_1158384b386f3db121a17380761ee079.pdf