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 \frac{d\rho}{dt} = -i[H,\rho] - \lambda \nabla_B \Phi[\rho] drives the state toward regions of minimal information degradation, defined by the functional \Phi[\rho], 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 \lambda>0 while recovering standard Lindblad dynamics as \lambda\to0. Under a Unitary Orthogonality Condition – exactly satisfied for pure dephasing and approximately in many-body localized phases – \Phi 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 \Phi \lesssim \gamma 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