Manifestly Covariant Herglotz-Coupled Dirac Equation in Curved Spacetime

We formulate an exact kinematic bridge unifying microscopic quantum fermion propagation with macroscopic open, nonconservative hydrodynamics by coupling the manifestly covariant Dirac equation in curved spacetime to the Herglotz-based manifestly covariant divergence law. By projecting the Dirac equation along a macroscopic fluid flow four-velocity and employing product-bundle connection rules, the convective spinor derivative is isolated without auxiliary densities or metric ansätze. Incorporating the bimetric determinant scaling bridge and this divergence law explicitly integrates macroscopic thermodynamic variables, specifically the applied power density, rest-frame isotropic pressure, and rest-frame mass density, directly into the Dirac equation. This first-principles framework demonstrates that microscopic fermion propagation is governed by fluid expansion or compression, bimetric determinant scaling, and open, nonconservative thermodynamic backreaction along the fluid congruence.