Information-Geometric Gradient Flows on the Bures Manifold and Decoherence-Free Subspaces

We formulate a geometric extension of open quantum dynamics in which the density matrix evolves as a Riemannian gradient flow on the Bures manifold. The evolution equation ddt = -iH, - B drives the state toward regions of minimal information degradation, defined by the functional, the instantaneous rate of relative-entropy change under the bare Lindbladian. This deterministic flow preserves trace and positivity, and introduces a single new universal constant >0 while recovering standard Lindblad dynamics as 0. Under a Unitary Orthogonality Condition – exactly satisfied for pure dephasing and approximately in many-body localized phases – becomes a Lyapunov functional, and its critical points (decoherence-free subspaces) are asymptotically stable attractors. Applied to disordered spin chains, the framework reproduces the known entropy‑suppression scaling N (J/W) ². The theory offers a falsifiable, information‑geometric principle where quantum states intrinsically minimise their own information loss. Keywords: quantum information geometry, Bures metric, gradient flow, Lindblad dynamics, decoherence-free subspaces, many-body localization, Lyapunov functional