Re: Configurational Entropy Problem

On 30 íj, 20:35, eal...@xxxxxxxxxxxx wrote:
Hello all, I am a scientist but not a mathematician by any means and I
have a problem I am having difficulty figuring out. I am trying to
describe the configurational entropy of a random arrangement of
objects. Say I have x red balls and y blue balls. If I want to
arrange these ball randomly in space, I believe that the number of
possible distinguishable configurations is the same as if I were to
place them on a regular lattice of x+y points, which would be (x+y)!/x!
y!. This should be correct because all points, although not at a
discrete position in space, are still equivalent (let me know if I am
wrong on this).

My dilemma comes when I want to distinguish that each of the two
species has a different number of nearest neighbors (NNs). The x red
balls has z NNs while the y blue balls have z' NNs. The type of NN
does not matter. I don't think now that the expression above is
correct, because now each point at which an ball is placed is not
equivalent to the others.

If someone come shed some light on this problem of mine, it would be
much appreciated.

Thanks so much,

Eric L.

Proposed formula depends only on counts, thus it will give equal
results for all possible arrangements. It were necessary to evaluate
numbers of triples (rrr, brr, rrb, brb, bbb, rbb, bbr, rbr),
eventually effect of ends (0b, b0, 0r, r0) in arrangements.
kunzmilan

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