The Thermodynamics of the Van Der Waals Black Hole Within Kaniadakis Entropy

In this work, we have studied the thermodynamic properties of the Van der Waals black hole in the framework of the relativistic Kaniadakis entropy. We have shown that the black hole properties, such as the mass and temperature, differ from those obtained by using the the Boltzmann–Gibbs approach. Moreover, the deformation <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>κ</mi></semantics></math></inline-formula>-parameter changes the behavior of the Gibbs free energy via introduced thermodynamic instabilities, whereas the emission rate is influenced by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>κ</mi></semantics></math></inline-formula> only at low frequencies. Nonetheless, the pressure–volume (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>P</mi><mo>(</mo><mi>V</mi><mo>)</mo></mrow></semantics></math></inline-formula>) characteristics are found independent of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>κ</mi></semantics></math></inline-formula> and the entropy form, unlike in other anti-de Sitter (AdS) black hole models. In summary, the presented findings partially support the previous arguments of Gohar and Salzano that, under certain circumstances, all entropic models are equivalent and indistinguishable.