Holographic heat engine in Horndeski model with the $k$-essence sector

We study the extended thermodynamical properties of the charged black hole in Horndeski model with the $k$-essence sector. Then we define a holographic heat engine via the black hole. We compute the engine efficiency in the large temperature limit and compare the results with the exact ones. With the given specified parameters in the rectangular engine, the higher order coupling suppresses the engine efficiencies.