Synchronization of thermodynamically consistent stochastic phase oscillators
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911533493125120 |
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| author | Chudak, Maciej Esposito, Massimiliano Ptaszynski, Krzysztof |
| author_facet | Chudak, Maciej Esposito, Massimiliano Ptaszynski, Krzysztof |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_09718 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Synchronization of thermodynamically consistent stochastic phase oscillators Chudak, Maciej Esposito, Massimiliano Ptaszynski, Krzysztof Statistical Mechanics 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. |
| title | Synchronization of thermodynamically consistent stochastic phase oscillators |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2512.09718 |