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继续讨论统计物理问题【6】
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继续讨论统计物理问题【6】
I already answered your questions in my previous message.
Our approach should be completely new to you.
You have to work through the algebra in my 2004 and 2006 papers, to convince yourself that it is a generic method, and those two equations are indeed equivalent.
If there is a difficulty, let me know.
You have to work through the algebra in my 2004 and 2006 papers, to convince yourself that it is a generic method, and those two equations are indeed equivalent.
If there is a difficulty, let me know.
Here is a recent preprint by my students discussed the connection of our approach to Ito and Stratonovich, which may be of some help.
Relation of Biologically Motivated New Interpretation of Stochastic Differential Equations to Ito Process.
Jianghong Shi, Tianqi Chen, Ruoshi Yuan, Bo Yuan, Ping Ao. submitted
http://arxiv.org/PS_cache/arxiv/pdf/1111/1111.2987v1.pdf
Relation of Biologically Motivated New Interpretation of Stochastic Differential Equations to Ito Process.
Jianghong Shi, Tianqi Chen, Ruoshi Yuan, Bo Yuan, Ping Ao. submitted
http://arxiv.org/PS_cache/arxiv/pdf/1111/1111.2987v1.pdf
Yours,
××××××××××××××××××××××××××××××××××××××××
Thanks for your email.
Thanks for your email.
I attached a file again. In terms of your explanation and the papers, I can't see the (stochastic) uncertainty to appear in the potential function therefore I think it is hard to suitable both equilibrium and non-equilibrium statistical processes, since the (stochastic) uncertainty in your model should be one of origins for the irreversibility. See attached file.
Best Regards,
AApendex(见上：提出二个随机微分方程的问题）
In the stochastic differential equations (SDEs),
is a deterministic force, is a Gaussian-white noise term with zero mean, etc. While after transformation, SDEs can become
,
where the matrix S is positive semi-definite and symmetric, the matrix T antisymmetric.
Question 1: Are both equations equivalent with each other?
Question 2: Is the potential function deterministic or deterministic plus stochastic?
×××××××××××××××××
On Fri, Mar 23, 2012 at 5:59 AM, < aoping@sjtu.edu.cn > wrote:
Thanks for your pointed questions.
I think I understoo them.
The answers to your first question is YES .
See my 2004 J. Phys A paper; also 2006 J. Phys. A paper (with Yin).
See my 2004 J. Phys A paper; also 2006 J. Phys. A paper (with Yin).
The for your second question,
If you read my above papers (if needed, also my 2008 Communication in Theoretical Physics paper), the answer is clear:
It is the same potential function (or Hamiltonian) in physics.
Generally a smooth function.
If you read my above papers (if needed, also my 2008 Communication in Theoretical Physics paper), the answer is clear:
It is the same potential function (or Hamiltonian) in physics.
Generally a smooth function.
Let me know if I have not answered your questions.
Yours
发送时间: 星期五, 2012年 3 月 23日 上午 9:28:13
See attached file.
Best regards,
On Tue, Mar 13, 2012 at 7:15 PM, < aoping@sjtu.edu.cn > wrote:
Good.
(1) Will hear your critique on our work after you have read them.
(2) If you think Prigogine can do it, it would be nice to learn their work. This would be great for others to learn the power of your approach. In fact, you have not provided their work to show I would be wrong.
And, I would be happy to be shown wrong here.
And, I would be happy to be shown wrong here.
Again, as far as I know, the impossibility for limit circle was stated in their own work.
(3) Yes, I am interested to know the problems solved. In pushing such goal, we may be able to move the field forward.
Pehraps I should state, which I think it is a professional standard when commenting others' work, I have read the major work of Prigogine school.
Of course, I could miss some important their work, which I would be happy to learn.
Of course, I could miss some important their work, which I would be happy to learn.
https://blog.sciencenet.cn/blog-266190-551197.html
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