2012/01/27 by I. V. Ovchinnikov, Ovchinnikov, Igor V.
Earth and Planetary Sciences · Physics and Astronomy · #Biological Physics (physics.bio-ph) #Chaotic Dynamics (nlin.CD) #Earth Systems and Cosmic Evolution #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Mathematical Physics (math-ph) #Quantum chaos and dynamical systems #Statistical Mechanics and Entropy
paper · pdf · doi:10.48550/arxiv.1201.5840
openalex publication_date 2012/01/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Previously, there existed no clear explanation why chaotic dynamics is always accompanied by the infinitely long memory of perturbations (and/or initial conditions) known as the butterfly effect (BE). In this paper, it is shown that within the recently proposed approximation-free supersymmetric theory of stochastic (partial) differential equations (SDE), the BE is a derivable consequence of (stochastic) chaos, a rigorous definition of which is the spontaneous breakdown of topological supersymmetry that all SDEs possess. It is also discussed that the concept of ergodicy must be refined under the condition of the spontaneous breakdown of pseudo-time-reversal symmetry when the model has "physical" states of multiple eigenvalues that survive the physical limit of the infinitely long temporal propagation.