Wikipedia:Articles for deletion/Supersymmetric theory of stochastic dynamics

Supersymmetric theory of stochastic dynamics

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This page fails the notability test. Searches of the literature show that this concept has been introduced and is being studied by a single author. The corresponding articles have hardly any citation on Google Scholar, besides self-citations. Hairer (talk) 04:10, 21 June 2017 (UTC)[reply]

Note: This debate has been included in the list of Mathematics-related deletion discussions. Hairer (talk) 04:10, 21 June 2017 (UTC)[reply]

Vasilii Tiorkin (talk) 22:36, 21 June 2017 (UTC) The concept of supersymmetric stochastic quantization of stochastic differnetial equations (SDEs) has been introduced by Parisi and Sourlas almost 40 years ago, that is, almost the same time as the supersymmetry itself. This concept is a very well known construction in theoretical physics. It is much less known in mathematics community, however, to which User:Hairer is likely to belong, which explains why he believes that this concept is brand new. The original paper by Parisi and Sourlas alone has over thousand citations.[reply]

It is true that the theory in the page is actually a generalization of Parisi-Sourlas approach who considered Langevin SDE only. STS applies to all SDEs. This is indeed relatively new knowledge. Only 6 years old to be exact. In this case, the following passage from "Wikipedia:What wikipedia is not" clearly applies: "... If you have completed primary research on a topic, your results should be published in other venues, such as peer-reviewed journals, other printed forms, open research, or respected online publications. Wikipedia can report your work after it is published and becomes part of accepted knowledge; however, citations of reliable sources are needed to demonstrate that material is verifiable, and not merely the editor's opinion." This is exactly the passage that made me decide that writing a page on the theory is an appropriate move. This passage is also the reason why I wrote this page only now in 2017 and not 6 years ago, when I published the first paper on this subject. To be specific, the theory now is published in the following peer-reviewed scientific resources:

1) Physical Review E 83, 051129 (2011). https://doi.org/10.1103/PhysRevE.83.051129

2) Chaos 22, 033134 (2012). http://dx.doi.org/10.1063/1.4746037

3) Chaos 23, 013108 (2013). http://dx.doi.org/10.1063/1.4775755

4) Modern Physics Letters B 30, 1650086 (2016). https://doi.org/10.1142/S021798491650086X

5) Phys. Rev. D 93, 085023 (2016). https://doi.org/10.1103/PhysRevD.93.085023

6) Entropy 18, 108 (2016). http://doi.org/10.3390/e18040108

7) Handbook on Applications of Chaos Theory, Eds. C. H. Skiadas and C. Skiadas (CRC/Taylor & Francis Group, 2016), pp. 271-305. https://doi.org/10.1201/b20232-21

All these are physical journals/book, so that mathematicians may not know about it. Nevertheless, the amount of the already published material on the generalization of Parisi-Sourlas approach to all SDEs in combination with all the previous work by other followers of Parisi and Sourlas clearly indicates that this theory deserves a separate wikipage.

It must be stressed at this point that covering recent results (itemized above) is a necessity. The point is that the most important finding from the supersymmetric approach to stochastic dynamics is the rigorous mathematical definition of the concept of dynamical chaos, over-a-century old dynamical phenomenon originally found by H.Poincare. The mathematical definition of chaos has never been found even for deterministic case (Devaney set of properties is not a definition). STS not only offers a rigorous definition for deterministic chaos but also generalize it to stochastic case, which is most important from the physical point of view as all real dynamical systems are stochastic. This finding is of ultimate scientific importance for all dynamics related disciplines. If we choose not to mention the recent work, this most valuable and interesting finding will be left out and there will be not much to talk about on the page. Such a page would not certainly be interesting to a general public, which is probably one of the reasons why wikipage on Parisi-Sourlas approach to only Langevin SDEs (that are never chaotic) did not exist before. — Preceding unsigned comment added by Vasilii Tiorkin (talk • contribs) 18:14, 22 June 2017 (UTC)[reply]

Comment – The subject material of the article as written appears to be more narrow than the title would indicate. For example, applying supersymmetric methods to solve the Fokker–Planck diffusion equation is a standard technique (covered, e.g., in Rifken's textbook, and in texts on supersymmetric quantum mechanics). Ditto the connection between supersymmetry and Onsager reciprocity; supersymmetry and fluctuation-dissipation relations; people have also made connections between supersymmetry and the Jarzynski equality, and other things I'm probably not thinking of at the moment. I would suggest returning this article to Draft space, until such time as it can be rewritten to better reflect a cross-section of what researchers actually mean when they put "supersymmetry" and "stochastic dynamics" together. XOR'easter (talk) 20:36, 21 June 2017 (UTC)[reply]

Vasilii Tiorkin (talk) 22:37, 21 June 2017 (UTC) I agree with the above comment that more references on the previous works must be made. In my excuse, many wiki-editors have experience in writing scientific papers and know that the work on the detailed list of publications is the last stage of the job. That was exactly my strategy - to write the "meat" first and, then, the detailed list of publications. As of now, Gozzi's, Kurchan's, Neimi's works etc. are underrepresented at this moment. Furthermore, the link e.g. supersymmetric nonlinear sigma models is very weak. Once again, these are on to do list. If given a little time, I will cover this gap. Also, thank you for the hint on Jarzynski equality. This brings the discussion to yet another excuse why the progress on the page is slow: the theory is extremely multidisiplinary, it has connections to multiple concept many of which have pages in wikipedia. Therefore, it is going to take a while before all the relevant links (and citations) are made properly. — Preceding unsigned comment added by Vasilii Tiorkin (talk • contribs) 22:32, 21 June 2017 (UTC)[reply]

Reply to comment – Perhaps it would be best to organize the article chronologically, starting with Parisi and Sourlas and ending with STS. XOR'easter (talk) 15:28, 22 June 2017 (UTC)[reply]

Vasilii Tiorkin (talk) 20:34, 22 June 2017 (UTC) Thank you. This is a good idea. I will write a section on the Parisi-Sourlas approach to Langevin SDEs and Gozzi's to classical mechanics before the STS part.[reply]