A common generator for Markov, Fokker-Planck and GKLS flows
We work in the universal information hydrodynamics (UIH) framework developed in two companion papers, in which reversible quantum dynamics and irreversible response are organised in a local metriplectic geometry driven by a convex free energy, a Fisher information metric, and an antisymmetric no-work channel. Within this setting the irreversible drift is always a Fisher gradient flow in a weighted H-1 geometry, equipped with a cost-entropy inequality and a curvature coercivity bound that are invariant under the addition of compatible reversible dynamics. In the present paper we show that this structure has a canonical realisation for Fokker-Planck equations, finite Markov chains and GKLS semigroups, and that it can be reconstructed operationally from process and state tomography on real quantum hardware.