Editing Stochastic differential equation (section)

== SDEs and supersymmetry ==
{{Main|Supersymmetric theory of stochastic dynamics}}

In supersymmetric theory of SDEs, stochastic dynamics is defined via stochastic evolution operator acting on the [[differential form]]s on the phase space of the model. In this exact formulation of stochastic dynamics, all SDEs possess topological [[supersymmetry]] which represents the preservation of the continuity of the phase space by continuous time flow. The spontaneous breakdown of this supersymmetry is the mathematical essence of the ubiquitous dynamical phenomenon known across disciplines as [[Chaos theory|chaos]], [[turbulence]], [[self-organized criticality]] etc. and the [[Goldstone theorem]] explains the associated long-range dynamical behavior, i.e., [[Butterfly effect|the butterfly effect]], [[Pink noise|1/f]] and [[Crackling noise|crackling]] noises, and scale-free statistics of earthquakes, neuroavalanches, solar flares etc.