Thermodynamics of rotating Bardeen black holes: Phase transitions and thermodynamics volume

We investigate the thermodynamical properties of the rotating Bardeen black holes characterized by mass m, the spin parameter a, and the magnetic charge g. We calculate exact expressions of the Hawking temperature, mass, entropy, and heat capacity. The black hole mass is minimum at radius r(+)(E), where both the heat capacity and temperature vanish with a stable remnant. Also, there exists a critical radius r(+)(C) of multiple orders, where the heat capacity diverges, suggesting that the black hole is thermodynamically stable in the range r(+)(E )< r(+), < r(+)(C). We also analyze the extended phase space thermodynamics of the rotating Bardeen-anti-de Sitter black holes. Treating the cosmological constant A and charge g as thermodynamic variables, we derive the generalized first law in the extended phase space to study the critical phenomena of the black holes. The Ehrenfest scheme for the P - V criticality of the rotating Bardeen black holes in anti-de Sitter spaces is examined. The Clausius-Clapeyron-Ehrenfest equations confirming the second-order phase transitions of the van der Waals fluid is no longer valid.