Energetics of stochastic limit-cycle oscillators: when does coupling reduce dissipation?

TL;DR

This study analytically explores how coupling in stochastic limit-cycle oscillators influences energy dissipation, revealing that Cartesian coupling consistently reduces dissipation regardless of system parameters.

Contribution

It provides analytical expressions for entropy production rate in coupled stochastic oscillators and shows Cartesian coupling always decreases dissipation.

Findings

Cartesian coupling reduces entropy production rate in all cases studied.

Effective temperature and system size significantly influence dissipation behavior.

Different coupling types affect velocity distributions and dissipation differently.

Abstract

Non-linear oscillators serve important functions in many biological systems, including within the inner ear and neuronal networks. The sustainment of oscillations in noisy environments requires continuous energy dissipation, quantified by the steady-state entropy production rate (EPR). We study an idealized, analytically tractable model of a stochastic circular limit cycle and examine how mutual coupling in pairs and populations alters dissipation. For a single oscillator, the EPR depends on three key factors: intrinsic frequency, tangential velocity fluctuations, and mean tangential velocity. The dynamics are characterized by a dimensionless effective temperature given by the ratio of intrinsic relaxation and diffusion timescales. For radial (amplitude), phase (Kuramoto-like), and Cartesian couplings, we derive analytical expressions for the EPR and confirm them numerically. Varying the effective temperature and system size strongly influences how the EPR depends on coupling strength and, in some cases, results in qualitatively distinct behaviors. Moreover, the coupling types affect the tangential velocity distributions differently. Notably, in all cases studied, Cartesian coupling reduces the EPR relative to the uncoupled system, irrespective of effective temperature and system size. The analysis of idealized non-linear oscillators reveals that different classes of coupling interactions and competing timescales present in the oscillators have distinct effects on energy dissipation.