Elementary derivation of the dissipation--coherence bound for stochastic oscillators

The dissipation–coherence bound is a conjectured tradeoff between entropy production and the quality of stochastic oscillations. We show that this tradeoff follows from the higher-order thermodynamic uncertainty relation together with a simple criterion on phase-current fluctuations. Moreover, in one-dimensional cyclic systems, this criterion is both necessary and sufficient for the dissipation–coherence bound. Our approach yields an elementary proof in the weak-noise Gaussian regime and extends naturally to some non-Gaussian systems, as illustrated by a run-and-tumble particle. We also compare current-based and spectral formulations of the dissipation–coherence bound.