Wikipedia:Articles for deletion/Supersymmetric theory of stochastic dynamics


 * The following discussion is an archived debate of the proposed deletion of the article below. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review).  No further edits should be made to this page.

The result was keep. (non-admin closure) Winged Blades Godric  06:09, 7 July 2017 (UTC)

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


 * 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.


 * It is true that the theory in the page is actually a generalization of Parisi-Sourlas approach. STS applies to all SDEs not only Langevin SDEs. This is indeed relatively new knowledge. 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 requirement is well satisfied as the generalization of the Parisi-Sourlas approach is now 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 the numerous previous works by the followers of Parisi and Sourlas in combination with the amount of the already published material on the generalization of the Parisi-Sourlas approach to all SDEs clearly indicate that this theory deserves a separate wikipage. It must be particularly stressed that covering the recent published results 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, the 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 generalizes it to stochastic case, which is most important from the physical point of view as all real dynamical systems are stochastic. This most notable finding is of ultimate scientific importance for all dynamics related disciplines. If we choose not to mention this most valuable result, a page would not potentially be interesting to a general public, which is probably one of the reasons why wikipage on the Parisi-Sourlas approach to only Langevin SDEs (that are never chaotic) did not exist before. In other words, new published results considerably improve notability of the subject — Preceding unsigned comment added by Vasilii Tiorkin (talk • contribs) 18:14, 22 June 2017 (UTC)


 * 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&#39;easter (talk) 20:36, 21 June 2017 (UTC)


 * 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. As of now, Gozzi's, Kurchan's, Neimi's works etc. are underrepresented. 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 multidisiplinary, it has connections to multiple concepts, many of which have pages in wikipedia. 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 to comment – Perhaps it would be best to organize the article chronologically, starting with Parisi and Sourlas and ending with STS. XOR&#39;easter (talk) 15:28, 22 June 2017 (UTC)


 * 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. Vasilii Tiorkin (talk) 00:29, 23 June 2017 (UTC) Just revised the page accordingly. Please see if you have any other useful suggestions.


 * The introductory paragraphs (the part before the Table of Contents) only talk about STS. This does not really indicate the history of the subject.  This text should come later, after the article explains earlier developments in supersymmetric theories of stochastic dynamics.  In general, the article is hard to follow; I do not think that, e.g., an advanced undergraduate student in physics would be able to get much out of it.  Even if the subject is advanced or esoteric, it should be possible to give a less advanced reader a better sense of where the subject matter lies within the general landscape of physics, and what other subjects are prerequisites for understanding it.  XOR&#39;easter (talk) 17:34, 23 June 2017 (UTC)


 * Vasilii Tiorkin (talk) 04:50, 24 June 2017 (UTC) Thank you. The first suggestion is incorporated. As to the general one, it is incorporated partly - a simple explanation in the introduction section is added and the number of mathematical expressions is reduced. I will keep working on making the presentation more readable, which feels like a long term project. Thank you once again and please let me know if you have more ideas on how to improve the page.


 * Vasilii Tiorkin (talk) 16:29, 26 June 2017 (UTC) The history of STS is covered and presented in the introduction, the page is organized chronologically, the connection to the nonlinear sigma model has a separate section, which is important because it is Witten and followers who worked out the algebro-topological meaning of the Parisi-Sourlas construction. The overall readability will be improved over time.


 * Comment this doesn't look like a properly formatted RfD, it looks like a copy of the talk page. If I understand the gist, there are enough references in the physics literature, but this is written for mathematicians so is more like original reasearch.  I'll suggest working it out on the talk page, then coming back here if you decide to delete later.  Smallbones( smalltalk ) 16:16, 28 June 2017 (UTC)

 Relisted to generate a more thorough discussion and clearer consensus.

Please add new comments below this notice. Thanks,  Sandstein   06:44, 29 June 2017 (UTC)

Both issues have been resolved. There are no reasons to delete. Keep the page. Vasilii Tiorkin (talk) 15:57, 29 June 2017 (UTC)


 * Weak Keep the article has severe problems but I see no case for deletion. Power~enwiki (talk) 03:31, 5 July 2017 (UTC)


 * The above discussion is preserved as an archive of the debate. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.