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Synchronization of thermodynamically consistent stochastic phase oscillators.

Maciej Chudak1, Massimiliano Esposito2, Krzysztof Ptaszyński1

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Summary
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This study models coupled stochastic oscillators, revealing a novel phase transition not governed by dissipation. Synchronization can decrease or increase dissipation, with unique divergent behaviors observed in fluctuations and entropy production.

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Area of Science:

  • Physics
  • Statistical Mechanics
  • Complex Systems

Background:

  • Coupled stochastic oscillators are fundamental in modeling complex systems.
  • The Kuramoto model describes synchronization in deterministic oscillators.
  • Understanding nonequilibrium phase transitions in stochastic systems is crucial.

Purpose of the Study:

  • To investigate a toy model of two kinetically coupled stochastic oscillators.
  • To analyze the continuous nonequilibrium phase transition between unsynchronized and synchronized states.
  • To explore the role of dissipation and information-theoretic quantities in synchronization.

Main Methods:

  • Modeling oscillator dynamics as a Markov jump process among N discrete phase states.
  • Analyzing the thermodynamic limit and large N behavior.
  • Characterizing universal scaling behavior of fluctuations and responses.
  • Investigating information-theoretic quantities like mutual information and information flow.

Main Results:

  • The model exhibits a continuous nonequilibrium phase transition.
  • Synchronization is not governed by an extremum dissipation principle; it can reduce or enhance dissipation.
  • Fluctuations and responses show divergent behavior with N near the phase transition.
  • Covariances of oscillator phases and local entropy productions diverge toward -∞, a novel phenomenon.
  • Mutual information and information flow act as order parameters for synchronization, displaying different scaling behaviors.

Conclusions:

  • The stochastic oscillator model provides insights into complex synchronization phenomena.
  • Nonequilibrium phase transitions in such systems exhibit unique characteristics beyond traditional thermodynamic principles.
  • Information-theoretic measures are effective in characterizing and quantifying synchronization in stochastic systems.