Fundamental Dynamic Structures III: The Dissipative Sector — Synchronization, Defect Clocks, and the Arrow of Time

We develop the dissipative sector of the Fundamental Dynamic Structures (FDS) program. Within the two-flow architecture of FDS I, the reduced dynamics of open subsystems is postulated (P7) to be the metric flow ẋ_diss = −M·∇F; this paper takes that structure as given and develops its phenomenology. **The numerical experiments reported here use a norm-projected dissipative LogSE as a phenomenological relaxation model (Appendix A); they illustrate defect-controlled phase ordering but do not constitute a simulation of the FDS Onsager operator M** — reconciling the two is part of the sector's central open problem, for which the Maas (dissipative) and Chow–Li–Zhou (Hamiltonian) discrete-transport geometries now provide a concrete mathematical route. Three results organize the sector. **(1) Two-ledger bookkeeping (interpretation):** under explicitly stated isothermal, no-work assumptions the reduced flow obeys dF_coarse/dλ = −𝒟 with 𝒟 = (∇F)ᵀM∇F ≥ 0; the decrease of coarse free energy is *interpreted* as compensated by entropy production in unresolved modes — a bath-balance derivation is not supplied here. Direction, duration, and observed causal order are treated as three distinct questions. **(2) Defect clocks (preliminary numerics):** in the phenomenological model, seeded wrapped topological content produces separation- and damping-dependent relaxation pathways and modifies global synchronization trajectories (topology-specific *local* ordering delay relative to matched controls is not yet demonstrated); first-zero census statistics (Fig. D1) show a fast channel whose mean event time among event runs grows with separation (0.40, 0.60, 1.00, 1.80 network units at d = 1.0–2.5, γ = 0.2; 4 seeds per point; horizon 30) and a surviving-or-unclassified channel whose weight increases with separation (survival/unclassified at horizon: 0/4 → 1/4 → 2/4 across d = 2.0–3.0; event times are census-disappearance times at output cadence Δλ = 0.2, core-trajectory classification pending); stronger damping accelerates the close-pair channel, while at d = 3.0 no census-disappearance event was observed before the horizon (3-seed observation). A hot random-phase start exhibits a **plaquette-winding foam** (raw wrapped census 3509 at initialization, collapsing to tens within the first smoothing stage and to ~7 by λ = 3 as synchrony rises); classification of wrapped windings into persistent physical cores is pending, so the vacuum-fluctuation analogy is kept in the discussion, not among results. We introduce **defect lifetime and integrated defect exposure (𝒜_wrap now, 𝒜_core after core classification) as candidate measures of relaxational age** in open FDS subsystems; their derivation from the P7 Onsager structure, calibration against relational clock time t_C (FDS I, Sec. 9), and connection to microscopic entropy production remain open. **(3) Past-directed evolution admits three readings** in the reduced description — ontological (the past is a former configuration of the one network, not a place), dynamical (the forward reduced law is Lyapunov-oriented), and informational (coarse-grained irreversibility) — of which only the first two are established here; gradient flows are generally invertible over finite intervals, so information loss requires a non-injective subsystem reduction that this paper does not construct. Contrast class: the present deterministic prototype contains no CSL-like stochastic momentum-diffusion term — a structural distinction from standard (non-dissipative) collapse models; no quantitative laboratory signature is claimed. The derivation of P7 from network microdynamics is the sector's central open problem.