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Elementary derivation of the dissipation-coherence bound for stochastic oscillators

Artemy Kolchinsky*

  • *Contact author: artemyk@gmail.com
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Phys. Rev. E 114, L012104 – Published 28 July, 2026

DOI: https://doi.org/10.1103/yj2t-frgz

Abstract

The dissipation-coherence bound is a conjectured trade-off between entropy production and the quality of stochastic oscillations. We show that this bound can be derived by combining the higher-order “thermodynamic uncertainty relation” with a simple condition on phase-current fluctuations. In one-dimensional cyclic systems, our proposed condition is shown to be equivalent to the dissipation-coherence bound itself. Our approach yields an elementary proof in the weak-noise Gaussian regime and extends naturally to some non-Gaussian systems, as we illustrate with a run-and-tumble particle. Finally, we contrast current-based and spectral formulations of the dissipation-coherence bound.

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Outline

Information

Phys. Rev. E 114, L012104– Published 28 July, 2026
  • Received 12 January 2026
  • Revised 27 March 2026
  • Accepted 2 June 2026
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