Complex eigenvalues of Markov generators are localized by cycle affinity and winding numbers, yielding thermodynamic bounds on relaxation modes and proving the Uhl-Seifert ellipse conjecture.
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Time-averaged observables exhibit kink or higher-order derivative singularities at supercritical Hopf bifurcations because phase averaging eliminates odd powers of the limit-cycle amplitude while the squared amplitude varies smoothly.
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Cycle affinity and winding localize eigenvalues of Markov generators
Complex eigenvalues of Markov generators are localized by cycle affinity and winding numbers, yielding thermodynamic bounds on relaxation modes and proving the Uhl-Seifert ellipse conjecture.
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Singular Behavior of Observables at Hopf Bifurcations
Time-averaged observables exhibit kink or higher-order derivative singularities at supercritical Hopf bifurcations because phase averaging eliminates odd powers of the limit-cycle amplitude while the squared amplitude varies smoothly.