Quantum Hydrodynamics and Fisher Information Geometry
We study irreversible response for coarse-grained densities in Fisher-regularised quantum hydrodynamics, working within a local metriplectic framework. The state space, boundary class, and uniformly elliptic symmetric mobility G are fixed once and for all, and all constructions take place in the weighted H-1ρ(G) geometry. Three instantaneous objects are singled out: the realised irreversible drift generated by G, a cost-entropy inequality linking control cost to entropy production, and a curvature coercivity bound on the Fisher functional. All three are invariant under the addition of any reversible drift generated by an antisymmetric operator J satisfying a weighted Liouville constraint. Equality in the cost-entropy bound picks out a one-dimensional irreversible ray, and a simple equality dial quantifies the reversible content of a given evolution. Read together with the companion paper, the present results fix the local irreversible geometry compatible with the same Fisher-selected Schrödinger sector.