Arecchi F. T.
Physics Department, University and Istituto Nazionale di Ottica, Florence, Italy.
Chaos. 1991 Oct;1(3):357-372. doi: 10.1063/1.165847.
Kramers' 1940 paper and its successive elaborations have extensively explored the transition rate between two stable situations, that is, in the language of system dynamics, the transition between the basins of attraction of two stable fixed point attractors. In a nonequilibrium system some of the above conditions may be violated, either because one of the two fixed points is unstable, as in the case of transient phenomena, or because both fixed points are unstable, as in the case of heteroclinic chaos, or because the attractors are more complex than fixed points, as in a chaotic dynamics where two or more strange attractors coexist. Furthermore, there is recent experimental evidence of space-time complexity consisting in the alternate or simultaneous oscillation of many modes, each one with its own (possibly chaotic) dynamics. In all the above cases, coexistence of many alternative paths implies a choice, either due to noise or self-triggered by the same interacting degrees of freedom. A review of the above phenomena in the case of nonequilibrium optical systems is here presented, with the aim of stimulating theoretical investigation on these novel rate processes.
克莱默斯1940年的论文及其后续的详细阐述广泛探讨了两种稳定状态之间的跃迁速率，也就是说，用系统动力学的语言来讲，就是两个稳定不动点吸引子的吸引盆之间的跃迁。在非平衡系统中，上述某些条件可能会被违反，要么是因为两个不动点之一不稳定，如瞬态现象的情况，要么是因为两个不动点都不稳定，如异宿混沌的情况，要么是因为吸引子比不动点更复杂，如在存在两个或更多奇怪吸引子共存的混沌动力学中。此外，最近有实验证据表明存在时空复杂性，表现为许多模式的交替或同时振荡，每个模式都有其自身（可能是混沌的）动力学。在上述所有情况下，许多替代路径的共存意味着一种选择，这要么是由于噪声，要么是由相同的相互作用自由度自触发的。本文对非平衡光学系统中的上述现象进行了综述，旨在激发对这些新型速率过程的理论研究。
