Supersymmetric theory of stochastic dynamics: Difference between revisions

Revision as of 14:07, 5 June 2025

Revision as of 15:00, 5 June 2025

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and the theory of pseudo-Hermitian operators. It can be seen as an algebraic dual to the traditional set-theoretic framework of the dynamical systems theory, with its added algebraic structure and an inherent [[Supersymmetry#Supersymmetry in dynamical systems|topological supersymmetry]] (TS) enabling the generalization of certain concepts from [[Deterministic system|deterministic]] to [[Stochastic process|stochastic]] models. At the same time, it can be looked upon as a [[Topological quantum field theories|topological field theory]] of stochastic dynamics that reveals its various topological aspects.

STS seeks to give a rigorous mathematical derivation to several [[Universality class|universal]] phenomena of [[Stochastic process|stochastic dynamical systems]]. It identifies [[Spontaneous symmetry breaking|spontaneous breakdown of TS]], present in all stochastic models, as the stochastic generalization of [[chaos theory|chaos]]. In this view, STS proposes a notion that dynamical chaos is a form of [[Topological order|topological order]] -- a perspective long anticipated by the pioneers of the concept of [[complexity]]. As pointed out in Ref.

<ref>{{cite journal

| last = Uthamacumaran

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}}</ref> in the context of STS:

:''... chaos is counter-intuitively the "ordered" phase of dynamical systems. Moreover, a pioneer of complexity, Prigogine, would define chaos as a spatiotemporally complex form of order...''

Accordingly,STS theprovides theorya solid mathentical foundation for this picture and associates the corresponding long-range phenomena such as [[Pink noise|1/f noise]] and [[self-organized criticality]] with the [[Goldstone theorem]]. The theory also provides a potential explanation for [[Self-organized criticality|self-organized criticality]], interpreting it as a noise-induced chaos that occurs at the border of conventional chaos and dissappears in the absence of noise.

== Overview ==