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We show that traditional extremal evaluations of coherence resonance encounter a bathtub effect, characterized by a broad resonance valley, which can lead to statistical inaccuracies. To address this, we propose a logarithmic centroid extraction method, which filters out stochastic jitter and recovers the underlying adiabatic Kramers scaling with high linearity (R2\u2009&amp;gt;\u20090.95). Furthermore, we identify the physical boundary where this adiabatic approximation breaks down under the strong-noise limit. Extending our analysis to gap-junction coupled systems, we observe a noise-induced transition from sub-threshold physiological shivering (characterized by statistical correlation but negligible functional output) to macroscopic functional synchronization. Our results provide a mathematical framework for extracting optimal noise intensities in broad energy valleys and offer insights into how quiescent biological systems utilize stochastic fluctuations for functional recovery.<\/jats:p>","DOI":"10.1063\/5.0341643","type":"journal-article","created":{"date-parts":[[2026,10,9]],"date-time":"2026-10-09T12:49:11Z","timestamp":1791550151000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":0,"title":["Breakdown of adiabatic scaling and noise-induced functional synchronization in deeply quiescent excitable systems"],"prefix":"10.1063","volume":"36","author":[{"ORCID":"https:\/\/orcid.org\/0009-0002-0297-4442","authenticated-orcid":false,"given":"Yefan","family":"Wu","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, The University of Sydney, Sydney, NSW 2006 ,","place":["Australia"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2026,10,9]]},"reference":[{"key":"2026100908490833100_c1","doi-asserted-by":"publisher","first-page":"775","DOI":"10.1103\/PhysRevLett.78.775","article-title":"Coherence resonance in a noise-driven excitable system","volume":"78","year":"1997","journal-title":"Phys. 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