Synchronization of thermodynamically consistent stochastic phase oscillators

TL;DR

This paper models two coupled stochastic oscillators as a Markov process, revealing a nonequilibrium phase transition to synchronization, with universal fluctuation scaling and novel divergence phenomena in phase covariances and entropy production.

Contribution

It introduces a simple stochastic oscillator model that captures synchronization phenomena and uncovers universal scaling laws and divergence behaviors near the phase transition.

Findings

Identification of a continuous nonequilibrium phase transition.

Divergence of phase covariances and entropy production near criticality.

Different scaling behaviors of mutual information and information flow.

Abstract

We consider a toy model of two kinetically coupled stochastic oscillators whose dynamics is described as a Markov jump process among $N$ discrete phase states. For large $N$, it maps onto the deterministic two-oscillator Kuramoto model of synchronization. Despite its simplicity, we postulate its relevance for understanding more complex and realistic oscillator systems. In the thermodynamic limit, the model exhibits a continuous nonequilibrium phase transition between the unsynchronized and synchronized states. We show that this transition is not governed by any extremum dissipation principle -- depending on system parameters, synchronization may either reduce or enhance the dissipation. Close to the phase transition, we observe a divergent behavior of fluctuations and responses with $N$ and characterize their universal scaling behavior. In particular, the covariances of the oscillator phases and the local entropy productions are shown to diverge towards $-\infty$, a phenomenon that has not been reported before. Finally, we study the behavior of information-theoretic quantities, demonstrating that mutual information and information flow between oscillators display different scaling with $N$ in synchronized and unsynchronized states, and thus can act as order parameters of synchronization.