The Supersymmetric Origin of Chaos and its Hidden Topological Order

Abstract

Dynamical chaos is a term that encompasses a wide range of nonlinear phenomena such as turbulence, neuronal avalanches, weather patterns, and many others. However, despite much work in the field of chaos, its fundamental physical origin still remains not fully understood. In this perspective we report on recent studies showing that chaos is the realization of one of the most fundamental principles in physics: spontaneous symmetry breaking also known as spontaneous ordering. In the present context, the symmetry involved is a topological supersymmetry inherent to all continuous-time (stochastic) dynamical systems. Chaos is then truly a manifestation of order of topological origin potentially encoding a sort of long-range information hidden beneath its apparent unpredictability. We finally argue that this point of view may have far-reaching implications well beyond chaotic dynamics.