From Osher Doctorow
Petr Jizba of Czech Technical U. (Czech Republic) and Toshihico
Arimitsu of Tsukuba U. Japan in "Towards information theory for
q-nonextensive statistics without q-deformed distributions,"
cond-mat/0510092 v2 3 Feb 2006 prove that the maximum entropy
probability (distribution):
1) p_k = exp[W(u)/v - s]
where W(u) is the Lambert W, v is q - 1, u has form r exp(ry) with r =
k(q - 1)/q and s is Ei/q and y is Ei/k and Ei is 1 - log(-phi)q/(q - 1)
- qLAMBDA[Ei - <E>_q]/phi where <E>_q is the q-averaged value of energy
E.
So essentially the maximum entropy probability according to the most
advanced "mainstream" standards (a combination of Renyi and Khinchin
entrppy axiomatics) increases with W.
Comparing with the previous Sections, W increases with maximum entropy,
energy, range, drift from a constant crosswind, radial distance from
launch in different scenarios.
As Jizba et al point out, the Maximum Entropy principle yields
probability distributions with the least bias and minimum ignorance
about information not received by an Observer or recipient (p. 6 of
their paper).
Osher Doctorow
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