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Phase transitions and entropies for synchronizing oscillators.

Martin Bier1,2, Bartosz Lisowski1,3, Ewa Gudowska-Nowak1,4

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Area of Science:

  • Physics
  • Nonlinear Dynamics
  • Statistical Mechanics

Background:

  • Coupled oscillator systems exhibit complex emergent behaviors.
  • Competition between synchronization and diffusive processes is crucial in many physical systems.
  • Understanding phase transitions and entropy production is key to characterizing system dynamics.

Purpose of the Study:

  • To investigate phase transitions in a generic model of coupled oscillators.
  • To analyze the interplay between phase synchronization and diffusive effects.
  • To quantify entropy production in both finite and continuum models.

Main Methods:

  • Derivation of phase transition mechanisms in a finite-state model.
  • Quantitative analysis of order parameter behavior and symmetry breaking.
  • Application of continuum approximation and derivation of a potential Burgers' equation for many-state models.

Main Results:

  • A phase transition was identified in the finite-state model, characterized by symmetry breaking and a discontinuous order parameter derivative.
  • Synchronized pulses were found to be low-entropy structures that promote overall system entropy production.
  • In the continuum approximation, no phase transition occurred, but diffusive entropy production still dominated over shock-related entropy reduction.

Conclusions:

  • The study reveals distinct behaviors of coupled oscillators depending on the number of states, with phase transitions occurring in finite systems.
  • The findings highlight the role of synchronized states in facilitating entropy production, a key concept in thermodynamics.
  • The derived Burgers' equation provides a framework for understanding pulse propagation in large-scale oscillator networks.