Ubiquitous order known as chaos

• Published in: Chaos, solitons and fractals solitons and fractals, 2024-04, Vol.181, p.114611, Article 114611
• Main Author: Ovchinnikov, Igor V.
• Format: Article
• Language: English
• Subjects: Chaos; Supersymmetry; Symmetry breaking; Topology
• ISSN: 0960-0779; 1873-2887
• DOI: 10.1016/j.chaos.2024.114611

A close relation has recently emerged between two of the most fundamental concepts in physics and mathematics: chaos and supersymmetry. In striking contrast to the semantics of the word ‘chaos’, the true physical essence of this phenomenon now appears to be a spontaneous order associated with the breakdown of the topological supersymmetry (TS) hidden in all stochastic (partial) differential equations, i.e., in all systems from a broad domain ranging from cosmology to nanoscience. Among the low-hanging fruits of this new perspective, which can be called the supersymmetric theory of stochastic dynamics (STS), are theoretical explanations of 1/f noise and self-organized criticality. Central to STS is the physical meaning of TS breaking order parameter (OP). In this paper, we discuss that the OP is a field-theoretic embodiment of the ‘butterfly effect’ (BE) – the infinitely long dynamical memory that is definitive of chaos. We stress that the formulation of the corresponding effective theory for the OP would mark the inception of the first consistent physical theory of the BE. Such a theory, potentially a valuable tool in solving chaos-related problems, would parallel the well-established and successful field theoretic descriptions of superconductivity, ferromagnetism and other known orders arising from the spontaneous breakdown of various symmetries of nature. •The paper provides a concise review of a theory that reveals that dynamical chaos is a spontaneous order.•It is shown that the corresponding order parameter describes the butterfly effect.•It is discussed how this theory lays the foundation for the first consistent physical theory of the butterfly effect.•It is argued that in some cases, the butterfly effect may admit a holographic field-theoretic description.