Supersymmetric theory of stochastic dynamics: Difference between revisions

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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]]. ItAs associatespointed 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 dissappearsout in the absence of noiseRef.

<ref>{{cite journal

| last = Uthamacumaran

| first = Abicumaran

| title = A Review of Dynamical Systems Approaches for the Detection of Chaotic Attractors in Cancer Networks

| journal = Patterns

| volume = 2

| issue = 4

| pages = 100226

| year = 2021

| doi = 10.1016/j.patter.2021.100226

| pmid = 33982021

| pmc = 8085613

| url = https://www.sciencedirect.com/science/article/pii/S2666389921000404

| access-date = 2025-06-05

}}</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...''

The theory 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 ==