Joule–Thomson effect and efficiency of deformed AdS–Schwarzschild black hole in presence of quintessence

We study the Joule–Thomson expansion and extended thermodynamics of a modified black hole characterised by the parameters α α , β β , and σ σ . Analysis of the Hawking temperature, Joule–Thomson coefficient, inversion curves, and isenthalpic trajectories shows that these parameters significantly modify the heating–cooling behaviour and thermal stability of the system. The deformation parameter α α and control parameter β β shift the temperature minimum, enlarge the cooling region, and raise the inversion temperature, while σ σ produces a weaker but consistent influence. The heat-engine analysis reveals that α α enhances efficiency, whereas higher β β and σ σ reduce it. Overall, the results demonstrate that geometric deformation and quintessence jointly govern the unified thermodynamic structure of the black hole.