Dissipation bounds the coherence of stochastic limit cycles

Overdamped stochastic systems maintained far from equilibrium can display sustained oscillations with fluctuations that decrease with the system size. The correlation time of such noisy limit cycles expressed in units of the cycle period is upper-bounded by the entropy produced per oscillation. We prove this constraint for first-order nonlinear systems in arbitrary dimensions perturbed by weak, uncorrelated Gaussian noise. We then extend the result to important examples of more general stochastic dynamics, including electronic and chemical clocks, illustrating the practical relevance of the dissipation-coherence bound for electronic computing and thermodynamic inference.