Introduction to Supersymmetric Theory of Stochastics
Department of Electrical Engineering, University of California at Los Angeles, Los Angeles, CA 90095, USA
Academic Editors: Martin Eckstein and Jay Lawrence
Received: 31 October 2015 / Revised: 8 March 2016 / Accepted: 21 March 2016 / Published: 28 March 2016
Many natural and engineered dynamical systems, including all living objects, exhibit signatures of what can be called spontaneous dynamical long-range order (DLRO). This order’s omnipresence has long been recognized by the scientific community, as evidenced by a myriad of related concepts, theoretical and phenomenological frameworks, and experimental phenomena such as turbulence, 1/f
noise, dynamical complexity, chaos and the butterfly effect, the Richter scale for earthquakes and the scale-free statistics of other sudden processes, self-organization and pattern formation, self-organized criticality, etc
. Although several successful approaches to various realizations of DLRO have been established, the universal theoretical understanding of this phenomenon remained elusive. The possibility of constructing a unified theory of DLRO has emerged recently within the approximation-free supersymmetric theory of stochastics (STS). There, DLRO is the spontaneous breakdown of the topological or de Rahm supersymmetry that all stochastic differential equations (SDEs) possess. This theory may be interesting to researchers with very different backgrounds because the ubiquitous DLRO is a truly interdisciplinary entity. The STS is also an interdisciplinary construction. This theory is based on dynamical systems theory, cohomological field theories, the theory of pseudo-Hermitian operators, and the conventional theory of SDEs. Reviewing the literature on all these mathematical disciplines can be time consuming. As such, a concise and self-contained introduction to the STS, the goal of this paper, may be useful.
This is an open access article distributed under the Creative Commons Attribution License
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
Scifeed alert for new publications
Never miss any articles
matching your research from any publisher
- Get alerts for new papers matching your research
- Find out the new papers from selected authors
- Updated daily for 49'000+ journals and 6000+ publishers
Define your Scifeed now
Share & Cite This Article
MDPI and ACS Style
Ovchinnikov, I.V. Introduction to Supersymmetric Theory of Stochastics. Entropy 2016, 18, 108.
Ovchinnikov IV. Introduction to Supersymmetric Theory of Stochastics. Entropy. 2016; 18(4):108.
Ovchinnikov, Igor V. 2016. "Introduction to Supersymmetric Theory of Stochastics." Entropy 18, no. 4: 108.
Show more citation formats
Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.
[Return to top]
For more information on the journal statistics, click here
Multiple requests from the same IP address are counted as one view.