Quantum-corrected thermodynamics and plasma lensing in non-minimally coupled symmetric teleparallel black holes

Abstract

We investigate the thermodynamic and optical signatures of electrically charged black holes (BHs) in symmetric teleparallel gravity (STPG) with non-minimal electromagnetic coupling, incorporating quantum corrections and plasma dispersion effects. The BH solution, characterized by a coupling parameter $k$, generalizes the Reissner–Nordström spacetime through power-law modifications to electromagnetic terms in the metric function. We implement exponential corrections to the Bekenstein–Hawking entropy of the form $S=S_0+e^{-S_0}$ and derive quantum-corrected expressions for fundamental thermodynamic quantities including internal energy, Helmholtz and Gibbs free energies, pressure, enthalpy, and heat capacity. Our analysis reveals rich phase transition structures with second-order transitions occurring at critical horizon radii for specific coupling values, demonstrating enhanced thermodynamic instability under strong non-minimal coupling effects. The quantum-corrected Joule–Thomson expansion analysis identifies distinct cooling and heating regimes separated by inversion points that shift systematically with the coupling parameter $k$. We analyze the efficiency of heat engines operating in Carnot cycles, finding that electromagnetic charge enhances thermodynamic performance with efficiency values approaching 99% for optimal configurations in this geometry. Using the Gauss–Bonnet theorem, we derive analytical expressions for gravitational deflection angles in both vacuum and plasma environments, revealing how non-minimal coupling and plasma dispersion create frequency-dependent lensing signatures that differ substantially from general relativity predictions.