Dissipation Bounds the Coherence of Stochastic Limit Cycles.

Area of Science:

• Nonlinear dynamics
• Statistical physics
• Thermodynamics

Background:

• Overdamped stochastic systems far from equilibrium can exhibit sustained oscillations.
• Fluctuations in these systems typically decrease as system size increases.
• The relationship between oscillation coherence and energy dissipation in such systems is a key area of study.

Purpose of the Study:

• To establish an upper bound on the correlation time of noisy limit cycles in overdamped stochastic systems.
• To connect this bound to the entropy produced per oscillation.
• To explore the practical implications of this bound for various scientific and technological applications.

Main Methods:

• Mathematical proof for first-order nonlinear systems in arbitrary dimensions.
• Analysis of systems perturbed by weak, uncorrelated Gaussian noise.
• Extension of the derived constraint to more general stochastic dynamics.

Main Results:

• A proven constraint relating correlation time (in units of cycle period) to entropy production per oscillation.
• Demonstration that this dissipation-coherence bound holds for first-order nonlinear systems.
• Validation of the bound's applicability to systems like electronic and chemical clocks.

Conclusions:

• The entropy produced per oscillation fundamentally limits the coherence of noisy limit cycles in overdamped systems.
• This finding provides a universal thermodynamic constraint on the performance of oscillating systems.
• The dissipation-coherence bound is relevant for optimizing energy efficiency and information processing in areas such as electronic computing and thermodynamic inference.