Talk:Boltzmann distribution

message: Everyone has over-complicated things, at least in the introduction, by going way into applications. In reality, a Boltzmann probability distribution is purely a normalized mathematical function that doesn't have anything to do with the applications. Why not express the Boltzmann probability distribution (and/or Boltzmann probability density) quite simply at first, as a mathematical function. This would be good for the General Reader, a novice, someone who doesn't know much about physics at all. (You people are too busy discussing - or arguing about - things like Classical Mechanics and Quantum Mechanics that the general reader probably doesn't know anything about.) The key notion is "KISS" = "Keep It Simple, Stupid", at least in the beginning, for the General Reader.  To give a specific example, the Gaussian distribution (or Gaussian density) is expressed mathematically as f(x) = Kexp(-ax^2) where the K is a normalizing constant, and "a" is an arbitrary positive constant. This has nothing to do with the physical application; and in fact, it can be used in thousands of different applications. Likewise, for x greater than or equal to zero, there are many other probability densities that can be considered and applied, where K is a different normalizing constant for each one: f(x) = Kexp(-ax); f(x) = Kxexp(-ax); f(x) = Kxexp(-ax^2); f(x) = K(x^2)exp(-ax^2); and so forth. These distributions (densities) have various names, such as the Rayleigh distribution; the Boltzman distribution; the exponential distribution; and so forth. These can be applied in many other fields than in physics, statistical mechanics, etc. Once again, to summarize, the Boltzmann distribution should be explained in simple mathematical terms first - before moving on into all of the complications of the applications in physics - and with the recognition that the Boltzmann distribution can conceivably be used in entirely different realms of probability and statistics. 98.67.174.68 (talk) 17:02, 21 June 2009 (UTC)
replies: text: See the Wikipedia article on the Rayleigh Distribution: http://en.wikipedia.org/wiki/Rayleigh_distribution For a much more clear expositon of the mathematical properties of a Distribution, with the physics explained elsewhere.98.67.174.68 (talk) 17:11, 21 June 2009 (UTC)
thread_title:  Everyone has over-complicated things 

message: (relevant to user jheald)
I've read your comments and added some more of my own (see below)
You mention that the equation I supplied below might/should become like the Boltzmann distribution when there is infinite energy - One way I can get it to resemble the Boltzmann distribution is to take the probability of any given particle having energy (n) OR MORE
this is the same as the probability that any given particle has the   n th energy level filled with an energy quanta.
The equation for this would be:
probality that n th energy level is occupied =
     sum from x=n to x=q (q is the maximum energy) of p(x)
There fore using this (the above equation) does give a drop off in probability as n increases but the shape of the curve is not the same as inverse exponential (at least when q the total energy is finite)HappyVR 19:40, 12 February 2006 (UTC)
thread_title:  Re exponential decay..

message: If a picture paints a thousand words...  Could someone find a graph to illustrate the text.  It makes it much easier to visualise.  Thanks.--King Hildebrand 19:06, 5 August 2006 (UTC)
thread_title:  Illustration 

message: What does E' mean in the probability distribution near the bottom? Is it the derivative of E? With respect to what? Is it the total energy? --aciel 22:52, 2 April 2007 (UTC)
replies: text: I think it's just a dummy energy variable to integrate over. Dicklyon 23:53, 2 April 2007 (UTC)
thread_title:  Notation 

message: The basic assumption of thermal equilibrium, which is a requirement for this distribution to hold, appears to be missing from the article.  — Preceding unsigned comment added by 192.249.47.174 (talk) 19:19, 12 March 2012 (UTC)
replies: text: You mean the fact the Boltzmann distribution indicates that atoms in thermal equilibrium are more likely to be in states with lower energies? --Luke R001 (talk) 10:44, 7 April 2012 (UTC)
thread_title:  thermal equilibrium 

message: It appears to me that this describes concepts exactly identical to Maxwell–Boltzmann statistics. Am I missing something, or should these be merged? --Nanite (talk) 07:51, 7 August 2013 (UTC)
replies: text: Well, since nobody answered I'll answer for myself. :) Having been digging around some more it looks like I was certainly wrong that Boltzmann distribution refers to M-B statistics. About half the time it people mean to refer to a canonical ensemble. Anyway, this page would be better replaced with a disambiguation-ish page which points people in the right direction, as the technical content is better covered in the specific articles. I'm removing the merge tags and will soon replace this article with this draft in progress. Nanite (talk) 21:49, 21 January 2014 (UTC)
thread_title:  Identical to Maxwell–Boltzmann statistics? 

message: This section seems irrelevant.  Negative absolute temperatures have been known and observed since the invention of the maser in the 1950's.  Either this section needs expansion and the relevance needs to be clarified, or it should be removed.  As it is, I see it as someone seeing the phrase "boltzmann distribution" in some popular news of the day, and in their ignorance adding it to the Wikipedia entry.  This section is 95% speculation and has no place here, imho.  Might just as well claim it could lead to perpetual motion.  Its PR Hype.72.172.11.222 (talk) 17:29, 30 September 2013 (UTC)
thread_title:  Inverted Boltzmann Distribution 

message: The rightmost curve in the Boltzmann distribution graph should read 1GeV, not 1eV.
https://en.wikipedia.org/wiki/File:Boltzmann_distribution_graph.svg  — Preceding unsigned comment added by 80.217.138.131 (talk) 17:30, 29 December 2015 (UTC)
thread_title:  Error in graph 

message: I 2nd the notion that this is a bad article. I'm not sure if I understand this plot correctly. Isn't the distribution discrete, why is x continuous? But I am not sure because x and lambda are funnily not defined in the article or the graphs subtitle. --194.39.218.23 (talk) 194.39.218.23 (talk) 12:55, 22 September 2023 (UTC)
thread_title:  Unlabelled graph