Recent content by rabbed

Thanks, i'll try that. If anyone has ideas for an analytic solution, just shoot :)

How would one go about solving this for a and b given N, E and K? n(0) + n(1) + … + n(K) = N n(0)*0 + n(1)*1 + … + n(K)*K = E Where n(k) = InverseDigamma(Digamma(a+1)-b*k)-1

Doh! So simple, thanks!

funny, But what values to put in? Around x=1 it seems to get y=200 e^(ln(600)-1/(1.381×10^-23*300)) = 0?

Hello Can anyone explain what formula (or parameters) was used to create the exponential Boltzmann distribution in fig 2a of this document? http://image.sciencenet.cn/olddata/kexue.com.cn/upload/blog/file/2009/5/20095251352697121.pdf I figure it must be something like y=e^(ln(600)-b*x) for some b?

Thank you for answering! Seen as a strictly mathematical problem (N distinct balls in K distinct boxes labeled with increasing integer scores) there is an actual right answer/distribution with a probability, so why wouldn’t we want that instead of relying on some random answer that depend on how...

I think the issue is that there should really be another constraint - that the ni’s should be integers. Otherwise the answers won’t make much physical sense (non-integer occupancy numbers). We’re relying on the Digamma function coming from a Gamma function which can be defined in multiple ways...

Hi With the exact Boltzmann distribution, ni = InverseDigamma(-α-β*εi)-1: https://studyres.com/doc/269738/revision-of-boltzmann-statistics-for-a-finite-number-of-p... Shouldn't I be able to get (n0, n1, n2, n3, n4, n5, n6, n7) = (6, 3, 2, 0, 0, 0, 0, 0) for some α and β, if N=11, E=7 and Δε=1...

Yes, I can't find the actual paper either but that abstract (as well as another abstract from him) makes the derivation clear: digamma(ni+1) = a-b*ei use approximation digamma(x+1) = ln(e^-m+x) where m = 0.5772156649 ln(e^-m+ni) = a-b*ei e^-m+ni = e^(a-b*ei) ni = e^(a-b*ei)-e^-m ni =...

Hi How do I use this formula: ni = (e^(B*(eH-ei))-1)*e^(-0.5772156649..) from this paper? https://ui.adsabs.harvard.edu/abs/2018DDA...49P...2C/abstract According to this site, (n0,n1,n2,n3,n4,n5,n6,n7) = (3,2,1,1,0,0,0,0) for N=7: https://bouman.chem.georgetown.edu/S02/lect21/lect21.htm Does...

I believe the most probable macrostate (for 6 particles, constant energy 6) is achieved with occupancy 3,1,1,1,0,0,0 in energy levels 0,1,2,3,4,5,6. Is the solution to take the outputs from the following calculation (where I've picked suitable values a=-0.06 and b=1.96 to fit the solution, but...

I would like to see a derivation of the exact Maxwell-Boltzmann distribution shown as (16) in this document: https://www.researchgate.net/publication/222670999_Exact_Maxwell-Boltzmann_Bose-Einstein_and_Fermi-Dirac_Statistics This is my starting point (f being the function to maximize, g and h...

With N objects, if I arrange each without replacement into K distinct partitions in which different object orders should not be accounted for: - For distinct objects I get a total number of Wtot = K^N ways to partition them, and a specific distribution with N1 objects in partition 1, N2 objects...

Nevermind.. It helped seeing indexing (treat identical as distinct) and faculty division (of the number of objects considered identical) as a means of adding and removing order into account of the number of ways. We can distribute N distinct balls into one box in 1 way (if we don’t care about...

Still having some issues with this. Could you say something more about the reasoning why (1 | 2A 2B) and (1 | 2B 2A) should count as just one "number of ways" instead of two? Is there any way to practically get the number of ways? Would it help to make some trials manually and create a PMF?