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arXiv · 2606.08801

Fluctuation-stable generalized entropy probes of spectral heterogeneity

Arpita Goswami
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Abstract

Generalized entropy measures are widely used to characterize localization and multifractality, and the regime \(q>1\) is often empirically found to exhibit improved numerical stability and cleaner scaling behavior. Here, we develop a fluctuation-stability framework for generalized entropy diagnostics and show that weak-amplitude spectral fluctuations are amplified for \(q<1\) and suppressed for \(q>1\), thereby providing a theoretical basis for the physically robust \(q>1\) regime. A thermodynamic scaling analysis further identifies an asymptotically stable regime beyond a critical threshold. As an application, we introduce the entropy-gradient susceptibility \(\chi_q\) as a coarse-grained probe of spectral heterogeneity. Using the Aubry-Andr\'e and generalized Aubry-Andr\'e models, we demonstrate that \(\chi_q\) sharply distinguishes homogeneous localization transitions from mobility-edge coexistence regimes. Our results establish fluctuation stability as a guiding principle for generalized entropy diagnostics in quasiperiodic systems.

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BibTeXRIS

Arpita Goswami. 2026-06-07. Fluctuation-stable generalized entropy probes of spectral heterogeneity. https://doi.org/10.1016/j.physleta.2026.131989

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