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arXiv · 2604.23752

The Diagnostic Disagreement and the Closure Failure of the Quiet-Sun Corona Are the Same Relative Entropy

Victor Edmonds
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Abstract

In the weakly collisional quiet-Sun corona, the electron distribution departs from Maxwellian, and ``the electron temperature'' is not single-valued: two standard diagnostics differ by a stable factor $R \approx 2.4$ across the solar cycle. We show this departure is a single relative entropy whose two orthogonal components are the EUV--radio diagnostic disagreement and the failure of the local conductive closure. By the generalized Pythagorean identity for Bregman divergences, the relative entropy of the $\kappa \approx 2.5$ distribution from its radio-diagnostic Maxwellian projection ($1.20$ nats) partitions with no cross-term into two components. The first is the energy-matched closure deficit ($0.32$ nats), the information discarded by the local Spitzer--H\"{a}rm closure (Edmonds 2026c), which itself has no convergent form across $\kappa \in [2,3]$. The second is the inter-projection diagnostic gap ($0.876$ nats), what the EUV and radio diagnostics disagree by and a closed-form function of $R$ within the shape envelope. Closure failure and diagnostic disagreement are therefore the same relative entropy in two orthogonal coordinates: together they account for the corona's full departure from Maxwellian. The physical heat flux that survives is non-local and tail-dominated. Any mechanism that sets this $\kappa$ must act on the suprathermal tail, operate non-locally, and fix $\kappa$ to the observed band; of the standalone candidates only velocity filtration (Scudder 1992) meets the first two, and whether it, or anything, fixes $\kappa$ is the open problem we leave posed.

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Victor Edmonds. 2026-04-26. The Diagnostic Disagreement and the Closure Failure of the Quiet-Sun Corona Are the Same Relative Entropy. https://arxiv.org/abs/2604.23752

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