Talk:Master equation

This article is rated Start-class on Wikipedia's content assessment scale. It is of interest to the following WikiProjects:

Physics Mid‑importance This article is within the scope of WikiProject Physics, a collaborative effort to improve the coverage of Physics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.PhysicsWikipedia:WikiProject PhysicsTemplate:WikiProject Physicsphysics Mid This article has been rated as Mid-importance on the project's importance scale. Statistics Low‑importance This article is within the scope of WikiProject Statistics, a collaborative effort to improve the coverage of statistics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.StatisticsWikipedia:WikiProject StatisticsTemplate:WikiProject StatisticsStatistics Low This article has been rated as Low-importance on the importance scale.

The chapman-kolmogorov equation is important enough to be by itself.

Rewritten a little, to indicate that master equations in physics are only a subset of Chapman-Kolmogorov equations. The focus of interest in the objects is also rather different.

IMO, the two articles should not be merged. -- Jheald 21:34, 10 November 2005 (UTC)Reply

I just skimmed the new articles, I agree. I think you can safely/unilaterally remove the merge tags, I don't think anyone will complain.linas 22:50, 10 November 2005 (UTC)Reply

Why is it called "MASTER"-equation? -- Ehsel —Preceding unsigned comment added by Ehsel (talk • contribs) 15:08, 21 February 2008 (UTC)Reply

Good question, it seems to be like the God particle -- pure made-for-TV science nomenclature. 84.227.227.112 (talk) 07:54, 14 April 2014 (UTC)Reply

I've heard also "balance equation". Might be nice begin transitioning from "master" to "balance" or some other term. Wefatherley (talk) 22:23, 25 November 2020 (UTC)Reply

Please do not start in with right-wing politics on science pages. It's called the "master equation" because the word "master" has a rather specific dictionary definition dating back to medieval Latin. Type in "etymology of master" into a search engine. 67.198.37.16 (talk) 18:11, 24 May 2024 (UTC)Reply

The literature often refers to Non Markovian Master Equations (see e.g. arXiv:quant-ph/0312103), while the definition in this article is clearly Markovian. Might there be a more general definition of a Master Equation, or does the descriptor "non Markovian" make it a different term, as in the Quantum Liouville Equation Cederal 13:51, 17 April 2007 (UTC)Reply

The ME is still Markovian if the transition rates at time t depend explicitly on t, i.e. dP/dt=A(t) P. In that case the Markov property P(x0,t0|x1,t1; x2,t2) = P(x0,t0|x1,t1) for t0>t1>t2 holds. Furthermore, the non-Markovian integro differential equation does not prevent ${\displaystyle P_{i}}$ from becoming negative.133.65.54.177 (talk) 06:27, 10 August 2011 (UTC)Reply

Is the FP equation really a generalisation of the Master equation? Obviously it deals with continuous things but there are systems where the FP equation is inaccurate while the ME covers everything, though they are obviously discrete in nature (chemical networks for instance). Perhaps the comment could be clarified so make it clear what the generalisation is in regards to, as someone might think that the FP equation is ALWAYS superior to the ME, which isn't the case. If someone wants examples I can give paper references illustrating this. AlphaNumeric (talk) 12:07, 5 March 2012 (UTC)Reply

It is, more or less. Sort-of. More precisely, it is also one of the four Kolmogorov equations. The Fokker-Planck equation deals with forward-time, where the noise term is continutiout, i.e. is not a jump process. This its mostly used for talking about diffusion. There the backwards equations are for when you don't know the distribution. The "true generalization" is really the Kolmogorov equations; but for practical applications, you retreat to the notation that's comfortable for you. It's quite the overlapping mess, since lots of people use this, with subtly different notation. I don't know how to put this in the article, so I put it here. 67.198.37.16 (talk) 23:14, 6 May 2025 (UTC)Reply

I tried to make the explanation tighter and clearer, while still addressing the "naive" concern about the order of the indices in a user-friendly way. 84.227.227.112 (talk) 07:52, 14 April 2014 (UTC)Reply

Nicely done! yoyo (talk) 04:22, 15 November 2015 (UTC)Reply

The section titled "Examples of master equations" unfortunately lacks any! It does point us to classical physics, saying it has "many" examples. And it does discuss two generalisations at length, with the first - the Lindblad equation - also discussed more extensively than it is in the (more appropriate) section on "Quantum master equations".

Please consider:

• restructuring this article to either list or discuss "Generalisations" in a separate section; and
• whether this article should also merge the content of the Quantum master equation article, to reduce redundant repetition.

(Should "reduce redundant repetition" be a WP style guideline "RRR"? ;-) ) yoyo (talk) 04:22, 15 November 2015 (UTC)Reply

I changed it because a system modelled by the master equation is not in exactly one state at a given time, but a probabilistic combination of them. The former is just a special case of the latter when all the probability mass is on one point and the master equation does not preserve that property. --Ricardohz (talk) 21:29, 2 November 2016 (UTC)Reply

IMO, this interpretation is confusing, especially since the article focuses primarily on the application of master equations to classical systems (there's other wikipedia articles on quantum master equations). The notion of a classical system being in a "probabilistic combination of states at a given time" is, at the very least, uncommon. The change should therefore be reverted and aligned to the first sentence in the introduction ("describing the [...] probability of a system to occupy [some state]" or "probability of finding a system in a certain state", ...) -- 2001:4CA0:0:F230:B49E:9A01:B8F6:F95E (talk) 12:42, 13 September 2017 (UTC)Reply

The first 20 hits in a search engine for "master equation" all state that it is about statistical Markovian processes; this is visible in the very first sentence shown in the hits, without even drilling deeper. Yes, classical mechanics is given by the equation ${\displaystyle {\frac {df}{dt}}=\{H,f\}}$ but this is called Hamilton's equation, and not the master equation, and the curly braces are the Poisson bracket. So although it "looks like" the master equation, its quite different. Yes, an essay could be written about how the "looks like" aspects are not just superficial, but this is a rather advanced topic. 67.198.37.16 (talk) 18:38, 24 May 2024 (UTC)Reply