Curvature-Induced Decoherence and Information Recovery

We develop a covariant open-system framework in which spacetime curvature directly governs the decoherence of quantum fields on curved backgrounds. Starting from a geometric deformation of the matter wavefunctional and using standard microlocal assumptions, we derive a curvature-dependent Lindblad equation whose local decoherence rate is fixed by scalar curvature invariants through the influence of metric fluctuations. Within this setting we establish a general purity-decay theorem: the reduced state seen by any semiclassical observer undergoes monotonic purity loss, and complete mixing occurs precisely when the curvature-dependent effective rate diverges. To characterize the associated information flow, we construct a geometric entropy func- tional inspired by Perelman’s H-entropy and show that it obeys a monotonicity relation under the induced information-theoretic flow. Finally, we explain how the semiclassical appearance of information loss produced by curvature-driven decoherence is reconciled with global unitarity once nonperturbative gravitational saddles—replica wormholes and quantum extremal surfaces—are included. The resulting picture integrates curvature-induced deco- herence, geometric entropy production, and the unitary Page curve into a single coherent framework.