Dissipative Quantum Gravity: Microscopic State Counting and Bekenstein-Hawking Entropy from Non-Hermitian Quantum Geometry

Abstract

Precise identification of microscopic states at event horizons clarifies the black hole information paradox. Dissipative Quantum Gravity (DQG) establishes a 2D non-Hermitian pseudospin-1/2 Chern insulator boundary lattice directly at the horizon screen. An open-system Lindblad dissipator links this lattice to a bipartite Hawking mode pair creation generator $H_0$, driving the horizon boundary dynamically to a second-order Exceptional Point ($EP_2$). Within this open-system framework, mode pair creation obeys a strict asymptotic saturation bound: $\lim_{t \to \infty} n_k(t) = 1/2$. Entanglement divergence terminates. Semiclassical radiation saturates. Microcanonical state enumeration across the $N_{\text{zero}} = C \times N_{\text{cells}}$ topological pseudospin zero-modes reproduces the exact Bekenstein-Hawking area law $S_{\text{BH}} = A/(4G_N)$. Simultaneously, fluctuations among the three $SO(3)$ horizon isometry zero-modes generate the universal logarithmic quantum correction $-\frac{3}{2}\ln(A/G_N)$.