Supersymmetric theory of stochastic dynamics

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Supersymmetric theory of stochastic dynamics (STS) is a multidisciplinary approach to stochastic dynamics on the intersection of dynamical systems theory, topological field theories, stochastic differential equations (SDE), 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 topological supersymmetry (TS) enabling the generalization of certain concepts from deterministic to stochastic models.

Using tools of topological field theory originally developed in high-energy physics, STS seeks to give a rigorous mathematical derivation to several universal phenomena of stochastic dynamical systems. Particularly, the theory identifies dynamical chaos as a spontaneous order originating from the TS hidden in all stochastic models. STS also provides the lowest level classification of stochastic chaos which has a potential to explain self-organized criticality.