Planck-scale deformation of thermodynamic topology and stability in Lifshitz black holes

Abstract We investigate the local thermodynamic stability and global thermodynamic topology of four-dimensional Lifshitz black holes with dynamical exponents z = 1 , 2 and horizon geometries k = + 1 , 0 , − 1 , including non-perturbative exponential entropy corrections. In the semiclassical regime, the z = 1 spherical sector is the only case with heat-capacity divergences, occurring for 0 < b ⩽ 1 / 36 ≃ 0.0278 , while the planar and hyperbolic sectors possess a single stable large-black-hole branch. The z = 2 sector is more robust: for b ⩾ 0 it is stable for r h > r 0 + ( b ) and shows no first-order phase transition in any geometry. Exponential corrections strongly modify only the most sensitive sectors. For z = 1 , k = + 1 , the instability window expands to 0 < b ⩽ 0.086559 for η = 0.5 and 0 < b ⩽ 0.205901 for η = 1 , while stronger corrections generate a richer multi-branch structure. The planar case develops only narrow correction-induced instability windows, the hyperbolic case remains essentially unchanged, and for