Synchronization of thermodynamically consistent stochastic phase oscillators

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.