Talk:Boltzmann factor

The image is broken. —Preceding unsigned comment added by Falc0n2600 (talk • contribs) 04:11, 22 February 2009 (UTC)

Derivation added

I felt the article could do with a little tidy, and I have added a derivation. Brings up the point that there is no page for the Gibbs factor - the "extension" of the B factor. I decided that the first equation didn't really explain what the Boltzmann factor was, so I included the probability formula. 94.193.2.213 (talk) 03:23, 24 June 2010 (UTC)

Hey! I think a derivation is absolutely necessary, but the one that's standing is not very much clear, at least to me. Imho the statement $\Omega _{E}\approx \Omega _{R}(E_{R})-\Omega _{S}(E_{S})$ could be explained in more detail. I think that a fundamental law should be derived from fundamental statements as, for example, it was done here. Don't get me wrong, it's a short elegant way to get the B-factor, but it is not easy to understand. So I would suggest to derive the long way as in the link above. --Xeltok (talk) 09:26, 17 February 2012 (UTC)

Unclear use of "Boltzamm constant"

The Boltzmann constant is described as:

$\beta ={\frac {1}{k_{B}T}}$

whereas Boltzmann's Constant is:

$k_{B}$

This appears to be inconsistent. Unless the first usage is widespread, I would suggest removing it, or at least discussing the discrepency. I am not an expert here, but the places I looked did not use the first form. Drevicko (talk) 10:05, 1 September 2010 (UTC)

They're two different things. The Boltzmann factor deals with state probabilities based on temperature and takes the Boltzmann factor as a parameter. The Boltzmann constant, on the other hand is - to quote wikipedia "the physical constant relating energy at the particle level with temperature observed at the bulk level." But I see what you mean, it does appear to be inconsistent. I think it's just an unnecessary typo - one could write "where beta is "etc"" - it's just a constant in the equation. Whiternoise (talk) 16:36, 11 September 2010 (UTC)

boltzmann's factor was for maxwell-boltzmann statistics, not canonical ensemble

At the moment the article seems to be describing the exponential factor exp(-ϵ_i/kT) in Gibbs' canonical ensemble, but as far as I'm aware Boltzmann's factor was actually the exp(-E_j/kT) of Maxwell-Boltzmann statistics. The two appear similar but actually refer to conceptually distinct concepts -- in the former case the ϵ_i refers to the total energy of an arbitrary many-body system in microstate i, whereas in the latter case E_j refers to the energy of one particle in a single-particle state j within an ideal gas.

Unless I'm missing something here, this article is mistitled and actually should redirect to Maxwell-Boltzmann statistics, whereas its content should be dropped or merged to canonical ensemble. --Nanite (talk) 15:50, 23 September 2013 (UTC)

Update: I see what's going on... digging around a bit I can see in earlier works (such as Tolman's 1938 Principles of Statistical Mechanics) the "Boltzmann ratio" just referred to the classical ideal gas case as intended by Boltzmann, however, in later works "Boltzmann factor" is used to refer to canonical ensemble (Reif's 1965 Fundamentals of Statistical and Thermal Physics as well as later popular textbooks). So, it looks like this conflation has fairly deep roots by now.

However, many of the articles linking here (e.g., polymer physics, band gap, excitation temperature, Curie's law) do use the Boltzmann factor in the original non-interacting particle statistics sense.

As a revised proposal, I'd make this article into a descriptive disambiguation-ish page: primarily to describe Boltzmann's non-interacting statistics case and forward the reader to Maxwell-Boltzmann statistics, and secondarily to mention the similar looking factor found in Gibbs' canonical ensemble. At the very least, there's no need for that loose derivation that can be found repeated on many other articles. --Nanite (talk) 09:08, 24 September 2013 (UTC)