Energetics of synchronization in coupled oscillators rotating on circular trajectories

TL;DR

This paper derives a general expression for energy dissipation in coupled oscillators on circular paths, revealing how coupling functions influence synchronization and energy use, with applications to biophysical systems.

Contribution

It introduces a unified stochastic thermodynamics framework for analyzing energy dissipation in coupled oscillators, highlighting the roles of coupling function components in synchronization.

Findings

Odd coupling parts decrease dissipation during synchronization.

Even parts cause square-root changes in dissipation near bifurcations.

Synchronization enhances the ability of oscillators to do work on the environment.

Abstract

We derive a concise and general expression of the energy dissipation rate for coupled oscillators rotating on circular trajectories by unifying the nonequilibrium aspects with the nonlinear dynamics via stochastic thermodynamics. In the framework of phase oscillator models, it is known that the even and odd parts of the coupling function express the effect on collective and relative dynamics, respectively. We reveal that the odd part always decreases the dissipation upon synchronization, while the even part yields a characteristic square-root change of the dissipation near the bifurcation point whose sign depends on the specific system parameters. We apply our theory to hydrodynamically coupled Stokes spheres rotating on circular trajectories that can be interpreted as a simple model of synchronization of coupled oscillators in a biophysical system. We show that the coupled Stokes spheres gain the ability to do more work on the surrounding fluid as the degree of phase synchronization increases.