Reduced Thermodynamic-Topological Observables for Multiscale Dissipative Systems. A fusion-relevant shell-model study of detection, design screening, and conservative operation

Abstract

We introduce a reduced set of thermodynamic-topological observables for ordered multiscale dissipative systems. An interface-local quadratic reduction produces bounded integrity and residual channels, a flux-force stability channel, a weighted path-graph bottleneck channel, and a coarse-graining drift indicator. The goal is practical rather than universal: a compact and interpretable layer of observables that can be computed repeatedly and compared across regimes. The main case study is a fusion-relevant MHD Sabra shell model. Across 400 synthetic anomalous-dissipation probes, the local Prigogine-style channel detects 400/400 events, while a composite alarm detects 399/400 with lower latency. When an OPCR trigger and an energy-collapse proxy are both observed within the same event, the earliest OPCR trigger leads the proxy by 11.29+/-13.49 model-time units on average (median 6.15, IQR [1.23, 17.22]; 255/313 early cases). A scan over 5000 coupling geometries raises the best log-Cheeger conductance from a baseline mean 0.07475+/-0.00171 to 0.09465 (+26.6%), whereas the current minimum-Phi geometry remains below the baseline mean. For operation, integrity-aware actuation and a conservative Phi-instrumented variant achieve 3.01x and 3.02x the recovery-per-unit-power efficiency of a uniform baseline. These numerics support a topology-first reading of the framework: hlog is credible as a Phase-1 design-screening observable, whereas Phi is presently best viewed as an operational or certification score. For fusion, the natural target is stellarator configuration screening, where magnetic topology dominates. A short appendix gives a toy neural-network portability check and is not used for the paper's main claims.

Figures (6)

• Figure 1: Workflow used in this paper. Ordered shells are reduced to interface-local quadratic statistics, from which thermodynamic, topological, and coarse-graining observables are extracted. For the present numerics, $h_{\log}$ is the Phase-1 design screen, while $\Phi$ is retained as an operational or certification score.
• Figure 2: Detection performance for the fusion surrogate. Left: detection rate with Wilson 95% intervals. Right: first-trigger latency summarized by the median and IQR. Thermodynamic channels occupy the high-reliability, low-latency corner; topological channels are weaker and slower as event detectors.
• Figure 3: Fusion-surrogate regime fingerprints in the $(p^\star,h_{\log})$ plane. Marker area scales with the coarse-graining indicator $\delta_F$ through a clipped $\log(1+\delta_F)$ map. The dashed horizontal line marks the baseline mean $h_{\log}$.
• Figure 4: Left: distribution of $h_{\log}$ over 5000 sampled geometries, with the baseline mean, the best screened design, and the current best-$\Phi$ design marked. Right: efficiency normalized to the uniform baseline. Text inside the bars reports mean absolute power and absolute efficiency $\eta$.
• Figure 5: Toy Transformer example. Curves show the mean over two seeds with min--max shading. Left: logged optimization objective (including the regularization term on OPCR update steps). Right: defect.

Theorems & Definitions (2)

• Proposition 1: Elementary invariants
• proof