N point particles move within a billiard table made of two circular cavities connected by a straight channel. The usual billiard dynamics is modified so that it remains deterministic, phase space volumes preserving and time reversal invariant. Particles move in straight lines and are elastically reflected at the boundary of the table, as usual, but those in a channel that are moving away from a cavity invert their motion (rebound), if their number exceeds a given threshold T. When the geometrical parameters of the billiard table are fixed, this mechanism gives rise to non-equilibrium phase transitions in the large N limit: letting T/N decrease, the homogeneous particle distribution abruptly turns into a stationary inhomogeneous one. The equivalence with a modified Ehrenfest two urn model, motivated by the ergodicity of the billiard with no rebound, allows us to obtain analytical results that accurately describe the numerical billiard simulation results. Thus, a stochastic exactly solvable model that exhibits non-equilibrium phase transitions is also introduced.

Deterministic reversible model of non-equilibrium phase transitions and stochastic counterpart / Cirillo, E. N. M.; Colangeli, M.; Muntean, A.; Richardson, O.; Rondoni, L.. - In: JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL. - ISSN 1751-8113. - 53:30(2020), p. 305001. [10.1088/1751-8121/ab94ec]

Deterministic reversible model of non-equilibrium phase transitions and stochastic counterpart

Cirillo E. N. M.;
2020

Abstract

N point particles move within a billiard table made of two circular cavities connected by a straight channel. The usual billiard dynamics is modified so that it remains deterministic, phase space volumes preserving and time reversal invariant. Particles move in straight lines and are elastically reflected at the boundary of the table, as usual, but those in a channel that are moving away from a cavity invert their motion (rebound), if their number exceeds a given threshold T. When the geometrical parameters of the billiard table are fixed, this mechanism gives rise to non-equilibrium phase transitions in the large N limit: letting T/N decrease, the homogeneous particle distribution abruptly turns into a stationary inhomogeneous one. The equivalence with a modified Ehrenfest two urn model, motivated by the ergodicity of the billiard with no rebound, allows us to obtain analytical results that accurately describe the numerical billiard simulation results. Thus, a stochastic exactly solvable model that exhibits non-equilibrium phase transitions is also introduced.
2020
billiards; Ehrenfest urn model; non-equilibrium states; phase transitions
01 Pubblicazione su rivista::01a Articolo in rivista
Deterministic reversible model of non-equilibrium phase transitions and stochastic counterpart / Cirillo, E. N. M.; Colangeli, M.; Muntean, A.; Richardson, O.; Rondoni, L.. - In: JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL. - ISSN 1751-8113. - 53:30(2020), p. 305001. [10.1088/1751-8121/ab94ec]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1458501
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