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-Nordstr & ouml;m 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 = S0 + eS0 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.