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

Global minimization via classical tunneling assisted by collective force field formation