Year: 2026
Type: article
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 toward -∞, 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.
Source: Physical review. E
DOI: 10.1103/3dhj-g2vz
Language: English
Subfield: Computer Networks and Communications
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: G5194357990, G5912056747, G808228963
OpenAlex ID: W4417292260