Complex Systems and Statistical Mechanics, Physics and Materials Science Research Unit, University of Luxembourg, L-1511 Luxembourg, Luxembourg.
Phys Rev E. 2019 Feb;99(2-1):022135. doi: 10.1103/PhysRevE.99.022135.
We study the stochastic dynamics of infinitely many globally interacting units made of q states distributed uniformly along a ring that is externally driven. While repulsive interactions always lead to uniform occupations, attractive interactions give rise to much richer phenomena: We analytically characterize a Hopf bifurcation which separates a high-temperature regime of uniform occupations from a low-temperature one where all units coalesce into a single state. For odd q, below the critical temperature starts a synchronization regime which ends via a second phase transition at lower temperatures, while for even q this intermediate phase disappears. We find that interactions have no effects except below critical temperature for attractive interactions. A thermodynamic analysis reveals that the dissipated work is reduced in this regime, whose temperature range is shown to decrease as q increases. The q dependence of the power-efficiency trade-off is also analyzed.
我们研究了由 q 个状态沿环均匀分布的无穷多个全局相互作用单元的随机动力学，这些单元受到外部驱动。虽然排斥相互作用总是导致均匀占据，但吸引相互作用会产生更丰富的现象：我们分析地描述了一个 Hopf 分岔，它将高温下的均匀占据状态与低温下所有单元合并成一个状态的状态分开。对于奇数 q，低于临界温度会出现同步状态，然后在较低温度下通过第二次相变结束，而对于偶数 q，中间相则消失。我们发现，除了吸引相互作用低于临界温度之外，相互作用没有影响。热力学分析表明，在这个状态下，耗散功减少，其温度范围随着 q 的增加而减小。还分析了功率效率权衡的 q 相关性。
