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Interacting particles in the Ehrenfest urn model exhibit phase transitions. Poincaré cycles and state duration times reveal the transition type and metastability.

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Area of Science:

  • Statistical Mechanics
  • Complex Systems

Background:

  • The Ehrenfest urn model describes particle distribution between two urns.
  • Interactions between particles introduce complex dynamics and phase transitions.

Purpose of the Study:

  • To investigate phase transitions in the Ehrenfest urn model with interacting particles.
  • To analyze relaxation times, Poincaré cycles, and state duration times.
  • To identify indicators for the nature of phase transitions and metastability.

Main Methods:

  • Calculated relaxation time to equilibrium.
  • Determined Poincaré cycles for equilibrium and far-from-equilibrium states.
  • Computed duration times of states during first-order phase transitions.

Main Results:

  • Scaling behavior of Poincaré cycles indicates the type of phase transition (first- or second-order).
  • Ratio of state duration times provides evidence for metastability in first-order phase transitions.

Conclusions:

  • Poincaré cycle scaling is a reliable indicator for phase transition classification.
  • Analysis of state duration ratios confirms metastability in first-order phase transitions within the Ehrenfest urn model.