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Transport and nonequilibrium phase transitions in polygonal urn models
Emilio N M Cirillo1, Matteo Colangeli2, Antonio Di Francesco2
1Dipartimento di Scienze di Base e Applicate per l'Ingegneria, Sapienza Università di Roma, via A. Scarpa 16, 00161 Roma, Italy.
Chaos (Woodbury, N.Y.)
|October 1, 2022
Summary
This study explores particle dynamics in a feedback-controlled system, revealing nonequilibrium phase transitions between homogeneous and inhomogeneous states. These findings offer insights into complex systems and biological feedback mechanisms.
Area of Science:
- Statistical Mechanics
- Nonlinear Dynamics
- Complex Systems
Background:
- Investigates deterministic dynamics of N point particles in a 2D billiard system.
- Features an active rectangular channel with a feedback control mechanism.
Purpose of the Study:
- To analyze nonequilibrium phase transitions in a feedback-controlled particle system.
- To explore the role of ergodicity in applying probabilistic theories.
- To connect theoretical predictions with numerical simulations and biological systems.
Main Methods:
- Deterministic dynamics simulation of N point particles.
- Analysis of a non-dissipative bounce-back mechanism preserving phase space volumes.
- Modeling of a closed circuit with active and passive channels.
Main Results:
- Identified nonequilibrium phase transitions between homogeneous and inhomogeneous phases in the large N limit.
- Demonstrated the possibility of a stationary current flow under specific conditions.
- Validated theoretical predictions against numerical simulation results.
Conclusions:
- The system exhibits complex emergent behaviors, including phase transitions, driven by feedback control.
- Ergodicity plays a crucial role in the applicability of probabilistic theories.
- The model provides a framework for understanding feedback control in biological systems.
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