Mathematical formalism of Joule-Thomson process for ADS-RN black hole coupled with non-linear electrodynamics field

We analyze the thermodynamic potentials and Joule-Thomson adiabatic expansion of a nonlinear electrodynamics charged AdS black hole. The negative cosmological constant is designated as thermodynamic pressure, while the geometrical mass is regarded as the enthalpy. In this study, we demonstrate the analogy between thermodynamic phase transitions in our considered black hole and Reissner-Nordstrom black hole systems, as well as discuss the influence of coupling parameters. The study confirmed the validity of the first law of black hole thermodynamics and the Smarr relation. We have established the Joule-Thomson thermodynamic coefficient and inversion temperature to conduct an analysis of Joule-Thomson adiabatic expansion. Also, the impact of charge parameters and nonlinear electrodynamic parameters on inversion curves have been investigated in detail. The isenthalpic and inversion curves are depicted to determine the cooling and heating regions, explicitly.