Magnetic black holes in AdS space with nonlinear electrodynamics, extended phase space thermodynamics and Joule--Thomson expansion

Thermodynamics of magnetically charged black holes in Anti-de Sitter space in an extended phase space is studied. The cosmological constant is considered as a pressure and the black hole mass is treated as the chemical entalpy. The black hole thermodynamics is similar to the Van der Waals liquid-gas thermodynamics. Quantities conjugated to the nonlinear electrodynamics parameter and a magnetic charge are obtained. The first law of thermodynamics and the generalized Smarr relation take place. We investigate critical behavior of black holes and Joule–Thomson expansion. The Gibbs free energy, the Joule–Thomson coefficient and the inversion temperature are calculated.