The Coherence‑Time Framework II: Local Transport, Currents, and Reaction–Diffusion Dynamics

The Coherence‑Time Framework II (OP2) develops the local, spatial dynamics of coherence within classical scalar field theory. Building on the global evolution law established in OP1, this work introduces the coherence current — a spatial flux that captures how structured, low‑entropy configurations redistribute themselves through a field. The paper derives a full reaction–diffusion equation for coherence density, separating three fundamental processes: - Conservative transport driven by spatial gradients - Reversible structure formation generated by constraints - Irreversible entropy production arising from damping and thermalisation This local transport law is shown to be fully consistent with the global coherence evolution equation of OP1, completing the transition from a global to a fully local field‑theoretic description of coherence dynamics. OP2 also analyses the transport coefficient \(D\), its dimensional structure, and its dependence on the underlying field dynamics. Explicit examples — including Gaussian pulses, dissipative spreading, driven growth, and steady‑state profiles — illustrate how coherence evolves under different physical regimes. Together, these results establish a unified framework for understanding coherence transport in classical fields and lay the groundwork for subsequent developments in the programme, including variational principles (OP3), gravitational coupling (OP4), quantum extensions (OP5), and cosmological applications (OP6).