Dissipation bounds the coherence of stochastic limit cycles

TL;DR

This paper establishes a fundamental limit on the coherence of stochastic limit cycles, showing that the entropy produced per cycle bounds the correlation time of oscillations in noisy, non-equilibrium systems.

Contribution

It proves a dissipation bound on the coherence of stochastic limit cycles for nonlinear systems and extends this to various stochastic dynamics relevant in electronics and chemistry.

Findings

Correlation time is bounded by entropy production per cycle.

The bound applies to diverse systems like electronic and chemical clocks.

Provides a theoretical framework linking thermodynamics and oscillation coherence.

Abstract

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.