Quantum corrections to thermodynamics of black holes with Chern-Simons term

Black hole thermodynamics offers a promising avenue for exploring the quantum nature of black holes and quantum gravity. We investigate the thermodynamic properties of dyonic black holes with Chern-Simons term. We demonstrate that the standard form of the first law of thermodynamics is inconsistent with the quantum statistical relation obtained from the saddle point approximation of the gravitational path integral. We manage to get the quantum correction through the theoretical and mathematical consistency. Our findings are corroborated by numerical tests and hydrodynamics.