Simple dynamical models can produce intricate behaviors in large networks. These behaviors can often be observed in a wide variety of physical systems captured by the network of interactions. Here we describe a phenomenon where the increase of dimensions self-consistently generates a force field due to dynamical instabilities. This can be understood as an unstable ("rumbling") tunneling mechanism between minima in an effective potential. We dub this collective and nonperturbative effect a "Lyapunov force" which steers the system towards the global minimum of the potential function, even if the full system has a constellation of equilibrium points growing exponentially with the system size. The system we study has a simple mapping to a flow network, equivalent to current-driven memristors. The mechanism is appealing for its physical relevance in nanoscale physics, and to possible applications in optimization, novel Monte Carlo schemes and machine learning.

翻译：简单的动态模型可以在大型网络中产生复杂的行为。 这些行为通常可以在互动网络所捕捉的各种物理系统中观察到。 我们在这里描述一个现象, 维度的增加自相矛盾地因动态不稳定而产生一个力场。 这可以被理解为在微型之间一个不稳定的( 隆隆的)隧道机制, 具有有效潜力。 我们把这种集体和非干扰效应说成是“ Lyapunov 力量 ”, 它将系统引向全球最小的潜在功能, 即使整个系统有一个平衡点星座随系统规模的大小而成倍增长。 我们研究的这个系统可以简单地映射到一个流动网络, 相当于当前驱动的分子。 这个机制在纳米物理学中, 以及可能应用到优化、 新的蒙特卡洛 计划和机器学习中。