Stability and thermodynamic topology of logarithmic nonlinear electrodynamics black holes with exponential entropy corrections

We investigate the thermodynamic stability and phase structure of black holes in logarithmic nonlinear electrodynamics (LNED) with non-perturbative exponential corrections to the Bekenstein–Hawking entropy. Classical thermodynamic quantities are derived from the Einstein–NED framework, and quantum corrections are incorporated consistently via the first law, yielding modified temperature and heat capacity. To characterize the global phase structure, we employ the thermodynamic-topology approach, where equilibrium states correspond to zeros of a thermodynamic vector field in the ( r + , Θ ) space, and stable/unstable branches appear as topological defects with opposite winding numbers. We find that the classical system exhibits two defects associated with stable and unstable branches. The exponential correction shifts the stable defect toward smaller horizon radii, while the large-radius branch remains nearly unaffected, preserving the total topological charge. These results show that non-perturbative quantum corrections primarily deform the near-horizon thermodynamics while maintaining the global topological structure, providing a unified framework for understanding the interplay between nonlinear electrodynamics, quantum corrections, and black-hole stability.