Black Hole Solution in Dehnen (1,4, 3 2)) Halo: Kaniadakis Entropy and Concerned Thermodynamics

We investigate the thermodynamic behavior and particle dynamics of the Dehnen [Formula: see text] black hole within the framework of Kaniadakis non-extensive entropy. The aim of this work is to explore how the combination of a realistic matter density profile and entropy deformation modifies the standard thermodynamic and dynamical properties of black holes. By incorporating the Kaniadakis entropy in place of the usual Bekenstein–Hawking entropy, we analyze the temperature, specific heat, Helmholtz free energy, and phase structure of the system. The temperature–entropy relation reveals a non-monotonic behavior with the appearance of temperature plateaus at large entropy, indicating suppressed thermal variation due to non-extensive statistical effects. Correspondingly, the specific heat exhibits multiple divergences, signaling second-order phase transitions and alternating thermodynamic stability regions that are absent in the classical Schwarzschild case. The analysis of Helmholtz free energy further reveals the formation of well-defined minima, demonstrating the existence of energetically favored equilibrium configurations and deformation-controlled global stability. The [Formula: see text]–[Formula: see text] diagram displays a multi-branch structure, indicating thermodynamic phase competition induced by the Kaniadakis parameter. In addition to thermodynamics, we investigate the geodesic structure of the spacetime. The effective potential for photon-like particles shows that the photon sphere becomes sensitive to the Dehnen density parameters, implying modifications in photon trapping regions and gravitational lensing properties. Furthermore, the angular momentum and specific energy of time-like particles reveal that the innermost stable circular orbit and orbital energetics depend explicitly on the matter density parameters. Unlike the Schwarzschild case, where orbital properties are universal, the Dehnen geometry introduces density-dependent orbital dynamics. Overall, our results demonstrate that the combined influence of Kaniadakis entropy and the Dehnen matter profile leads to a significantly richer thermodynamic phase structure and modified particle dynamics, offering new insights into the behavior of realistic astrophysical black holes.