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 simulatio...

中文翻译：

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非平衡相变和随机对应物的确定性可逆模型

N点粒子在台球桌内移动，该台球桌由通过直通道连接的两个圆形腔构成。修改了通常的台球动力学，以便保持确定性，保持相空间体积和时间反转不变。像往常一样，粒子沿直线移动并在工作台的边界处弹性反射，但是如果粒子的数量超过给定的阈值T，则远离腔的通道中的粒子会将其运动（反弹）反转。当台球桌的几何参数固定时，这种机制会在较大的N极限内引起非平衡相变：让T / N减小，均匀的颗粒分布突然变成静止的不均匀分布。修改后的Ehrenfest两模型的等效性，