Comment on "Dissipation bounds the coherence of stochastic limit cycles"

Abstract

Recent work has identified a fundamental bound on the thermodynamic cost of stochastic oscillators in the weak-noise regime (Santolin and Falasco, 2025; Nagayama and Ito, 2025). In this brief note, we provide an alternative and elementary derivation of this bound, based only on the assumption of Gaussian phase fluctuations and the thermodynamic uncertainty relation. Our approach may be useful for future generalizations of the bound.