Cirillo, E. N. M.; Colangeli, M.; Di Francesco, A.; Kröger, M.; Rondoni, L. Transport and Nonequilibrium Phase Transitions in Polygonal Urn Models. Chaos: An Interdisciplinary Journal of Nonlinear Science, 2022, 32, 093127. https://doi.org/10.1063/5.0101933.
Cirillo, E. N. M.; Colangeli, M.; Di Francesco, A.; Kröger, M.; Rondoni, L. Transport and Nonequilibrium Phase Transitions in Polygonal Urn Models. Chaos: An Interdisciplinary Journal of Nonlinear Science, 2022, 32, 093127. https://doi.org/10.1063/5.0101933.
Cirillo, E. N. M.; Colangeli, M.; Di Francesco, A.; Kröger, M.; Rondoni, L. Transport and Nonequilibrium Phase Transitions in Polygonal Urn Models. Chaos: An Interdisciplinary Journal of Nonlinear Science, 2022, 32, 093127. https://doi.org/10.1063/5.0101933.
Cirillo, E. N. M.; Colangeli, M.; Di Francesco, A.; Kröger, M.; Rondoni, L. Transport and Nonequilibrium Phase Transitions in Polygonal Urn Models. Chaos: An Interdisciplinary Journal of Nonlinear Science, 2022, 32, 093127. https://doi.org/10.1063/5.0101933.
Abstract
We study the deterministic dynamics of N point particles moving at constant speed in a 2D table made of two polygonal urns connected by an active rectangular channel, which applies a feedback-control on the particles, inverting the horizontal component of their velocities, when their number in the channel exceeds a fixed threshold. Such a bounce--back mechanism is non-dissipative: it preserves volumes in phase space. An additional passive channel closes the billiard table forming a circuit in which a stationary current may flow. Under specific constraints on the geometry and on the initial conditions, the large N limit allows nonequilibrium phase transitions between homogeneous and inhomogeneous phases. The role of ergodicity in making a probabilistic theory applicable is discussed both for rational and irrational urns. The theoretical predictions are compared with the numerical simulation results. Connections with the dynamics of feedback-controlled biological systems are highlighted.
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