Thermodynamic Control of Superradiance in a Charged Two-Dimensional Black Hole

Within the framework of gravitational thermodynamicization, we study charged scalar waves in static two-dimensional black-hole backgrounds. Starting from the scalar action, we derive the exact radial wave equation and show that a neutral, massless, minimally coupled field in a genuine two-dimensional spacetime has neither an angular barrier nor superradiant amplification. For a charged field, amplification is controlled by the electrostatic potential at the horizon. In the charged two-dimensional string black hole, this potential is related to the Hawking temperature, making the superradiant frequency window dependent on the thermodynamic state of the black hole. A near-horizon residue provides a coordinate-independent test of the superradiant threshold. With a reflecting outer boundary, we also obtain necessary frequency conditions and an upper bound on the growth rate of possible unstable modes. Numerical calculations confirm the flux relation and distinguish superradiant amplification from genuine instability.