Probing thermodynamics of Einstein–Maxwell scalar black hole through exponential corrected entropy

In this paper, we examine the thermodynamic properties and geometries of dilaton black hole in Einstein–Maxwell-scalar (EMS) theory. We use Bekenstein–Hawking entropy with exponential correction to calculate the mass and temperature of the black hole, as well as their stability through heat capacity (local) and Gibbs free energy (global). It is found that heat capacity and Gibbs free energy exhibit the stability/instability and phase transitions of aforementioned black hole according to various choices of charge parameter ($Q$). Several formalisms are used to examine the thermodynamic geometry of this black hole, including Weinhold, Ruppiner, Quevedo and HPEM metrics in order to investigate the microscopic picture and explain the attraction or repulsion of particles in stable/unstable regions of black hole.