Dynamics of Coherence Capacity: Transport, Concentration, and Exhaustion

We develop the dynamical theory of coherence capacity, the finite stability margin that allows a projection-based effective description to remain predictive. Building on the identification of coherence capacity as a conserved resource within admissible regimes, we show that it admits a local transport law and a divergence-free current inside coherence basins. We prove that persistent strain generically induces focusing of the capacity flow, leading to concentration, bottleneck formation, and exhaustion on codimension-one surfaces. At admissibility barriers, capacity is no longer conserved and effective evolution becomes noninvertible, yielding irreversibility as a structural necessity despite invertibility of the underlying dynamics. This transport-and-focusing picture provides the dynamical substrate for gravitational attraction, horizon formation, thermalization, and loss of memory, without modifying fundamental dynamics or introducing new degrees of freedom. The results are model-independent and follow solely from projection-based effective description with finite stability margins, completing the coherence-capacity framework by supplying its dynamics.