{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"5a4818bb79261c5dc22970da733b97d86c4ba141b3de1b6a5541bd55b09f119a","created":"2026-10-03T07:18:11Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"1f1738016b5be1cfe812296133cbfc47358bb797dc204c308c9ec0fd0b457542","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"stat.stochastic-thermodynamics.oscillation-coherence-cost","kind":"well-posed","literature_status":"partially-resolved","n":"1","parents":[],"plain":"Biochemical clocks, such as circadian oscillators in cells, keep time for only a limited number of cycles before noise scrambles them, and keeping them coherent costs free energy. A proposed universal minimum cost was disproved in 2026, and the correct universal bound is open.","posed_since":"2017","precise":"For a finite Markov jump network with stationary entropy production rate $\\sigma$ and second eigenvalue $-\\lambda_R + i \\lambda_I$ of the rate matrix, the conjecture $\\sigma \\ge \\lambda_I^{2}/\\lambda_R$ (arXiv:2112.01607) fails (counterexample arXiv:2609.34352), while a version weighted by an eigenvector-uniformity factor is proven (arXiv:2606.05498). Find the tightest bound on entropy produced per oscillation period in terms of the coherence of an observable correlation function $C(t)$ (number of oscillations before decay), and a model that saturates it.","problem_ref":null,"references":"","settled_by":"A proof of a bound in terms of observable correlation functions together with a saturating model.","status_note":"Shiraishi disproved the spectral conjecture in September 2026 (arXiv:2609.34352); Gu proved a weaker bound with a mode-uniformity factor that reduces to the original for translation-invariant rings (Phys. Rev. E 113, 064130, 2026).","title":"Minimal dissipation per coherent oscillation of a stochastic 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