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答复来自莫斯科的博士
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Date: Sat, 9 Jun 2007 05:41:10 -0700 (PDT)
From: "Leon Feng"
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Subject: Re: You paper has been cited by me
To: "Andrey Rostovtzev"
Dear Dr. Andrei
The basic idea of mine came from the fact.
Jaynes' Maximal Entropy Principle is based on the "Maximal Probability
of Occurrence Principle."
I argued that if the Maximal Probability of Occurrence Principle can determine
everything, the following questions will come:
The probability of occurrence P by itself cannot give distributions which
match experience. Why?
arctan(P) cannot give distributions which match experience. Why?
There are infinite functions which change monotonically with the probability
of occurrence. But Nature only chooses Boltzmann-Gibbs-Shannon entropy as
the target function for various classic extensive systems. Why ?
My answer is very simple. The General and Unified Constraints play the
role of "choosing one from infinity."
Just like you said that Nature has only limited types of distributions.
That is because Nature may only have limited types of General and Unified
Constraints.
For any classic distribution, the General and Unified Constraint has to
be
-p1ln(f1)-p2ln(f2)-...-pnln(fn) = Constant (which is Eq. (1) of my paper).
When the equilibrium distribution f is exponential distribution, this General
Constraint becomes
p1x1+p2x2+...+pnxn = constant.
I have given 4 examples in my paper, please read again.
Best Regards
Leon
Andrey Rostovtzev
Dear Dr Leon Xiangjun Feng,
thank you for the message. I apologies for a delay with my
response. It was not absolutely clear for me how the constraints make
a
choise for the form of entropy. Though I like this innovative idea.
Could you please give me few illustrative examples? Which constraints
are
needed for exponential statistical distribution (live examples)?
Best regards, Andrei.
On Sun, 13 May 2007, Leon Feng wrote:
> Dear Dr. Rostovtsev
>
> Your paper :
>
> arXiv:cond-mat/0507414 v1 18 Jul 2005
>
> has been cited by me.
>
> Please see
>
> http://www.arxiv.org/abs/0705.1332
>
> Best Wishes
>
> Leon Xiangjun Feng
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