Einstein Maxwell Scalar Black Hole: Thermodynamic Properties with Logarithmic Barrow Entropy

The thermodynamics of black holes (BHs) within the Einstein Maxwell Scalar (EMS) framework, incorporating Barrow entropy and its logarithmic corrections to analyze quantum gravity effects is investigated here. A static, spherically symmetric BH solution is obtained by coupling the scalar field nonminimally to the electromagnetic field through a scalar dependent function. The thermodynamic properties including temperature, specific heat, and Gibbs free energy are derived and explored in the context of Barrow-modified entropy. We identify phase transitions and critical behavior by analyzing PV criticality and uncover the influence of scalar and electric charges on stability. Furthermore, the Joule Thomson expansion is examined to understand the inversion behavior and thermodynamic responses under adiabatic expansion. Our findings suggest the presence of thermodynamic instabilities, remnants, and nontrivial critical phenomena, providing new insights into BH thermodynamics in modified gravity scenarios with quantum corrections.