Heat capacities and thermodynamic geometry in deformed Jackiw-Teitelboim gravity

We study the thermodynamics of charged AdS black holes in deformed Jackiw-Teitelboim (dJT) gravity and their phase structures. In this regard, we will find some critical values for the temperature, entropy and charge of the corresponding black holes. We also compute the heat capacities, expansion coefficient and isothermal compressibility as thermodynamic response functions and study their behaviors at the critical points. It will be shown that these variables satisfy the Ehrenfest's equations in the case of second-order phase transition. We employ different formalisms to investigate thermodynamic geometry, such as Weinhold, Ruppeiner and new thermodynamic geometry, then analyze the singularities of the thermodynamic curvatures in this context. We show that these singularities are also correspond to the divergences of the response functions which indicating the critical points of phase transitions.