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Small-amplitude synchronization in driven Potts models.

Jan Meibohm1,2, Massimiliano Esposito3

  • 1<a href="https://ror.org/03v4gjf40">Technische Universität Berlin</a>, Straße des 17. Juni 135, 10623 Berlin, Germany.

Physical Review. E
|November 20, 2024
PubMed
Summary
This summary is machine-generated.

Driven q-state Potts models show a dynamical phase transition to synchronization. Stable synchronized states minimize entropy production, revealing a linear dissipation-stability relation and a minimum-dissipation principle.

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Area of Science:

  • Statistical Mechanics
  • Complex Systems
  • Nonlinear Dynamics

Background:

  • Driven q-state Potts models exhibit complex dynamics.
  • Understanding phase transitions and synchronization in these systems is crucial.

Purpose of the Study:

  • Investigate the dynamical phase transition in driven q-state Potts models.
  • Characterize synchronization patterns and their relation to dissipation.

Main Methods:

  • Derivation of normal-form equations for high-dimensional Hopf bifurcations.
  • Exact solutions in the thermodynamic limit.
  • Exploitation of model symmetry to solve equations.

Main Results:

  • Discovery of a dynamical phase transition from decoherent oscillations to synchronization.
  • Uncovering intricate stable synchronization patterns and a rich phase diagram.
  • Demonstration that synchronization reduces dissipation, with stable states minimizing entropy production.

Conclusions:

  • A linear dissipation-stability relation connects entropy production and phase-space contraction near the phase transition.
  • A minimum-dissipation principle for driven Potts models is proposed, valid far from equilibrium.